Daily Papers

Guidance of generative models is typically achieved by modifying the probability flow vector field through the addition of a guidance field. In this paper, we instead propose the Source-Guided Flow Matching (SGFM) framework, which modifies the source distribution directly while keeping the pre-trained vector field intact. This reduces the guidance problem to a well-defined problem of sampling from the source distribution. We theoretically show that SGFM recovers the desired target distribution exactly. Furthermore, we provide bounds on the Wasserstein error for the generated distribution when using an approximate sampler of the source distribution and an approximate vector field. The key benefit of our approach is that it allows the user to flexibly choose the sampling method depending on their specific problem. To illustrate this, we systematically compare different sampling methods and discuss conditions for asymptotically exact guidance. Moreover, our framework integrates well with optimal flow matching models since the straight transport map generated by the vector field is preserved. Experimental results on synthetic 2D benchmarks, physics-informed generative tasks, and imaging inverse problems demonstrate the effectiveness and flexibility of the proposed framework.

In Image-to-Video (I2V) generation, a video is created using an input image as the first-frame condition. Existing I2V methods concatenate the full information of the conditional image with noisy latents to achieve high fidelity. However, the denoisers in these methods tend to shortcut the conditional image, which is known as conditional image leakage, leading to performance degradation issues such as slow motion and color inconsistency. In this work, we further clarify that conditional image leakage leads to overfitting to in-domain data and decreases the performance in out-of-domain scenarios. Moreover, we introduce Fourier-Guided Latent Shifting I2V, named FlashI2V, to prevent conditional image leakage. Concretely, FlashI2V consists of: (1) Latent Shifting. We modify the source and target distributions of flow matching by subtracting the conditional image information from the noisy latents, thereby incorporating the condition implicitly. (2) Fourier Guidance. We use high-frequency magnitude features obtained by the Fourier Transform to accelerate convergence and enable the adjustment of detail levels in the generated video. Experimental results show that our method effectively overcomes conditional image leakage and achieves the best generalization and performance on out-of-domain data among various I2V paradigms. With only 1.3B parameters, FlashI2V achieves a dynamic degree score of 53.01 on Vbench-I2V, surpassing CogVideoX1.5-5B-I2V and Wan2.1-I2V-14B-480P. Github page: https://pku-yuangroup.github.io/FlashI2V/

We propose DAVIS, a Diffusion-based Audio-VIsual Separation framework that solves the audio-visual sound source separation task through generative learning. Existing methods typically frame sound separation as a mask-based regression problem, achieving significant progress. However, they face limitations in capturing the complex data distribution required for high-quality separation of sounds from diverse categories. In contrast, DAVIS circumvents these issues by leveraging potent generative modeling paradigms, specifically Denoising Diffusion Probabilistic Models (DDPM) and the more recent Flow Matching (FM), integrated within a specialized Separation U-Net architecture. Our framework operates by synthesizing the desired separated sound spectrograms directly from a noise distribution, conditioned concurrently on the mixed audio input and associated visual information. The inherent nature of its generative objective makes DAVIS particularly adept at producing high-quality sound separations for diverse sound categories. We present comparative evaluations of DAVIS, encompassing both its DDPM and Flow Matching variants, against leading methods on the standard AVE and MUSIC datasets. The results affirm that both variants surpass existing approaches in separation quality, highlighting the efficacy of our generative framework for tackling the audio-visual source separation task.

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation remains largely unexplored. In this paper, we propose a novel 2D simulation that captures high-dimensional geometric properties in an interpretable 2D setting, enabling us to analyze the learning dynamics of flow matching during training. Based on this analysis, we derive several key insights about flow matching behavior: (1) density approximation can paradoxically degrade performance due to mode discrepancy, (2) directional alignment suffers from path entanglement when overly concentrated, (3) Gaussian's omnidirectional coverage ensures robust learning, and (4) norm misalignment incurs substantial learning costs. Building on these insights, we propose a practical framework that combines norm-aligned training with directionally-pruned sampling. This approach maintains the robust omnidirectional supervision essential for stable flow learning, while eliminating initializations in data-sparse regions during inference. Importantly, our pruning strategy can be applied to any flow matching model trained with a Gaussian source, providing immediate performance gains without the need for retraining. Empirical evaluations demonstrate consistent improvements in both generation quality and sampling efficiency. Our findings provide practical insights and guidelines for source distribution design and introduce a readily applicable technique for improving existing flow matching models. Our code is available at https://github.com/kwanseokk/SourceFM.

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate high-quality samples with fewer function evaluations, typically through iterative rectification methods or optimal transport solutions. In this paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Consistency-FM directly defines straight flows starting from different times to the same endpoint, imposing constraints on their velocity values. Additionally, we propose a multi-segment training approach for Consistency-FM to enhance expressiveness, achieving a better trade-off between sampling quality and speed. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models and 1.7x faster than rectified flow models while achieving better generation quality. Our code is available at: https://github.com/YangLing0818/consistency_flow_matching

Flow matching is a recent framework to train generative models that exhibits impressive empirical performance while being relatively easier to train compared with diffusion-based models. Despite its advantageous properties, prior methods still face the challenges of expensive computing and a large number of function evaluations of off-the-shelf solvers in the pixel space. Furthermore, although latent-based generative methods have shown great success in recent years, this particular model type remains underexplored in this area. In this work, we propose to apply flow matching in the latent spaces of pretrained autoencoders, which offers improved computational efficiency and scalability for high-resolution image synthesis. This enables flow-matching training on constrained computational resources while maintaining their quality and flexibility. Additionally, our work stands as a pioneering contribution in the integration of various conditions into flow matching for conditional generation tasks, including label-conditioned image generation, image inpainting, and semantic-to-image generation. Through extensive experiments, our approach demonstrates its effectiveness in both quantitative and qualitative results on various datasets, such as CelebA-HQ, FFHQ, LSUN Church & Bedroom, and ImageNet. We also provide a theoretical control of the Wasserstein-2 distance between the reconstructed latent flow distribution and true data distribution, showing it is upper-bounded by the latent flow matching objective. Our code will be available at https://github.com/VinAIResearch/LFM.git.

Flow matching has emerged as a promising framework for training generative models, demonstrating impressive empirical performance while offering relative ease of training compared to diffusion-based models. However, this method still requires numerous function evaluations in the sampling process. To address these limitations, we introduce a self-corrected flow distillation method that effectively integrates consistency models and adversarial training within the flow-matching framework. This work is a pioneer in achieving consistent generation quality in both few-step and one-step sampling. Our extensive experiments validate the effectiveness of our method, yielding superior results both quantitatively and qualitatively on CelebA-HQ and zero-shot benchmarks on the COCO dataset. Our implementation is released at https://github.com/VinAIResearch/SCFlow

Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time along its flow trajectory, and ignoring neighboring points. However, this pointwise approach may overlook correlations between points along the generation trajectory that could enhance velocity predictions, thereby improving downstream generation quality. To address this, we propose Graph Flow Matching (GFM), a lightweight enhancement that decomposes the learned velocity into a reaction term -- any standard flow matching network -- and a diffusion term that aggregates neighbor information via a graph neural module. This reaction-diffusion formulation retains the scalability of deep flow models while enriching velocity predictions with local context, all at minimal additional computational cost. Operating in the latent space of a pretrained variational autoencoder, GFM consistently improves Fr\'echet Inception Distance (FID) and recall across five image generation benchmarks (LSUN Church, LSUN Bedroom, FFHQ, AFHQ-Cat, and CelebA-HQ at 256times256), demonstrating its effectiveness as a modular enhancement to existing flow matching architectures.

Classifier-free guidance is a key component for enhancing the performance of conditional generative models across diverse tasks. While it has previously demonstrated remarkable improvements for the sample quality, it has only been exclusively employed for diffusion models. In this paper, we integrate classifier-free guidance into Flow Matching (FM) models, an alternative simulation-free approach that trains Continuous Normalizing Flows (CNFs) based on regressing vector fields. We explore the usage of Guided Flows for a variety of downstream applications. We show that Guided Flows significantly improves the sample quality in conditional image generation and zero-shot text-to-speech synthesis, boasting state-of-the-art performance. Notably, we are the first to apply flow models for plan generation in the offline reinforcement learning setting, showcasing a 10x speedup in computation compared to diffusion models while maintaining comparable performance.

Recently, Flow Matching models have pushed the boundaries of high-fidelity data generation across a wide range of domains. It typically employs a single large network to learn the entire generative trajectory from noise to data. Despite their effectiveness, this design struggles to capture distinct signal characteristics across timesteps simultaneously and incurs substantial inference costs due to the iterative evaluation of the entire model. To address these limitations, we propose Blockwise Flow Matching (BFM), a novel framework that partitions the generative trajectory into multiple temporal segments, each modeled by smaller but specialized velocity blocks. This blockwise design enables each block to specialize effectively in its designated interval, improving inference efficiency and sample quality. To further enhance generation fidelity, we introduce a Semantic Feature Guidance module that explicitly conditions velocity blocks on semantically rich features aligned with pretrained representations. Additionally, we propose a lightweight Feature Residual Approximation strategy that preserves semantic quality while significantly reducing inference cost. Extensive experiments on ImageNet 256x256 demonstrate that BFM establishes a substantially improved Pareto frontier over existing Flow Matching methods, achieving 2.1x to 4.9x accelerations in inference complexity at comparable generation performance. Code is available at https://github.com/mlvlab/BFM.

Unconditional flow-matching trains diffusion models to transport samples from a source distribution to a target distribution by enforcing that the flows between sample pairs are unique. However, in conditional settings (e.g., class-conditioned models), this uniqueness is no longer guaranteed--flows from different conditions may overlap, leading to more ambiguous generations. We introduce Contrastive Flow Matching, an extension to the flow matching objective that explicitly enforces uniqueness across all conditional flows, enhancing condition separation. Our approach adds a contrastive objective that maximizes dissimilarities between predicted flows from arbitrary sample pairs. We validate Contrastive Flow Matching by conducting extensive experiments across varying model architectures on both class-conditioned (ImageNet-1k) and text-to-image (CC3M) benchmarks. Notably, we find that training models with Contrastive Flow Matching (1) improves training speed by a factor of up to 9x, (2) requires up to 5x fewer de-noising steps and (3) lowers FID by up to 8.9 compared to training the same models with flow matching. We release our code at: https://github.com/gstoica27/DeltaFM.git.

Flow matching models have emerged as a powerful method for generative modeling on domains like images or videos, and even on irregular or unstructured data like 3D point clouds or even protein structures. These models are commonly trained in two stages: first, a data compressor is trained, and in a subsequent training stage a flow matching generative model is trained in the latent space of the data compressor. This two-stage paradigm sets obstacles for unifying models across data domains, as hand-crafted compressors architectures are used for different data modalities. To this end, we introduce INRFlow, a domain-agnostic approach to learn flow matching transformers directly in ambient space. Drawing inspiration from INRs, we introduce a conditionally independent point-wise training objective that enables INRFlow to make predictions continuously in coordinate space. Our empirical results demonstrate that INRFlow effectively handles different data modalities such as images, 3D point clouds and protein structure data, achieving strong performance in different domains and outperforming comparable approaches. INRFlow is a promising step towards domain-agnostic flow matching generative models that can be trivially adopted in different data domains.

Flow matching has recently emerged as a powerful alternative to diffusion models, providing a continuous-time formulation for generative modeling and representation learning. Yet, we show that this framework suffers from a fundamental instability in the low-noise regime. As noise levels approach zero, arbitrarily small perturbations in the input can induce large variations in the velocity target, causing the condition number of the learning problem to diverge. This ill-conditioning not only slows optimization but also forces the encoder to reallocate its limited Jacobian capacity toward noise directions, thereby degrading semantic representations. We provide the first theoretical analysis of this phenomenon, which we term the low-noise pathology, establishing its intrinsic link to the structure of the flow matching objective. Building on these insights, we propose Local Contrastive Flow (LCF), a hybrid training protocol that replaces direct velocity regression with contrastive feature alignment at small noise levels, while retaining standard flow matching at moderate and high noise. Empirically, LCF not only improves convergence speed but also stabilizes representation quality. Our findings highlight the critical importance of addressing low-noise pathologies to unlock the full potential of flow matching for both generation and representation learning.

Flow matching is a powerful framework for generating high-quality samples in various applications, especially image synthesis. However, the intensive computational demands of these models, especially during the fine-tuning process and sampling processes, pose significant challenges for low-resource scenarios. This paper introduces Bellman Optimal Step-size Straightening (BOSS) technique for distilling flow-matching generative models: it aims specifically for a few-step efficient image sampling while adhering to a computational budget constraint. First, this technique involves a dynamic programming algorithm that optimizes the step sizes of the pretrained network. Then, it refines the velocity network to match the optimal step sizes, aiming to straighten the generation paths. Extensive experimental evaluations across image generation tasks demonstrate the efficacy of BOSS in terms of both resource utilization and image quality. Our results reveal that BOSS achieves substantial gains in efficiency while maintaining competitive sample quality, effectively bridging the gap between low-resource constraints and the demanding requirements of flow-matching generative models. Our paper also fortifies the responsible development of artificial intelligence, offering a more sustainable generative model that reduces computational costs and environmental footprints. Our code can be found at https://github.com/nguyenngocbaocmt02/BOSS.

Conditional flow matching (CFM) has emerged as a powerful framework for training continuous normalizing flows due to its computational efficiency and effectiveness. However, standard CFM often produces paths that deviate significantly from straight-line interpolations between prior and target distributions, making generation slower and less accurate due to the need for fine discretization at inference. Recent methods enhance CFM performance by inducing shorter and straighter trajectories but typically rely on computationally expensive mini-batch optimal transport (OT). Drawing insights from entropic optimal transport (EOT), we propose Weighted Conditional Flow Matching (W-CFM), a novel approach that modifies the classical CFM loss by weighting each training pair (x, y) with a Gibbs kernel. We show that this weighting recovers the entropic OT coupling up to some bias in the marginals, and we provide the conditions under which the marginals remain nearly unchanged. Moreover, we establish an equivalence between W-CFM and the minibatch OT method in the large-batch limit, showing how our method overcomes computational and performance bottlenecks linked to batch size. Empirically, we test our method on unconditional generation on various synthetic and real datasets, confirming that W-CFM achieves comparable or superior sample quality, fidelity, and diversity to other alternative baselines while maintaining the computational efficiency of vanilla CFM.

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Furthermore, Flow Matching opens the door to training CNFs with other, non-diffusion probability paths. An instance of particular interest is using Optimal Transport (OT) displacement interpolation to define the conditional probability paths. These paths are more efficient than diffusion paths, provide faster training and sampling, and result in better generalization. Training CNFs using Flow Matching on ImageNet leads to consistently better performance than alternative diffusion-based methods in terms of both likelihood and sample quality, and allows fast and reliable sample generation using off-the-shelf numerical ODE solvers.

Diffusion models have revolutionized generative tasks through high-fidelity outputs, yet flow matching (FM) offers faster inference and empirical performance gains. However, current foundation FM models are computationally prohibitive for finetuning, while diffusion models like Stable Diffusion benefit from efficient architectures and ecosystem support. This work addresses the critical challenge of efficiently transferring knowledge from pre-trained diffusion models to flow matching. We propose Diff2Flow, a novel framework that systematically bridges diffusion and FM paradigms by rescaling timesteps, aligning interpolants, and deriving FM-compatible velocity fields from diffusion predictions. This alignment enables direct and efficient FM finetuning of diffusion priors with no extra computation overhead. Our experiments demonstrate that Diff2Flow outperforms na\"ive FM and diffusion finetuning particularly under parameter-efficient constraints, while achieving superior or competitive performance across diverse downstream tasks compared to state-of-the-art methods. We will release our code at https://github.com/CompVis/diff2flow.

Diffusion models, and their generalization, flow matching, have had a remarkable impact on the field of media generation. Here, the conventional approach is to learn the complex mapping from a simple source distribution of Gaussian noise to the target media distribution. For cross-modal tasks such as text-to-image generation, this same mapping from noise to image is learnt whilst including a conditioning mechanism in the model. One key and thus far relatively unexplored feature of flow matching is that, unlike Diffusion models, they are not constrained for the source distribution to be noise. Hence, in this paper, we propose a paradigm shift, and ask the question of whether we can instead train flow matching models to learn a direct mapping from the distribution of one modality to the distribution of another, thus obviating the need for both the noise distribution and conditioning mechanism. We present a general and simple framework, CrossFlow, for cross-modal flow matching. We show the importance of applying Variational Encoders to the input data, and introduce a method to enable Classifier-free guidance. Surprisingly, for text-to-image, CrossFlow with a vanilla transformer without cross attention slightly outperforms standard flow matching, and we show that it scales better with training steps and model size, while also allowing for interesting latent arithmetic which results in semantically meaningful edits in the output space. To demonstrate the generalizability of our approach, we also show that CrossFlow is on par with or outperforms the state-of-the-art for various cross-modal / intra-modal mapping tasks, viz. image captioning, depth estimation, and image super-resolution. We hope this paper contributes to accelerating progress in cross-modal media generation.

We introduce CaLMFlow (Causal Language Models for Flow Matching), a novel framework that casts flow matching as a Volterra integral equation (VIE), leveraging the power of large language models (LLMs) for continuous data generation. CaLMFlow enables the direct application of LLMs to learn complex flows by formulating flow matching as a sequence modeling task, bridging discrete language modeling and continuous generative modeling. Our method implements tokenization across space and time, thereby solving a VIE over these domains. This approach enables efficient handling of high-dimensional data and outperforms ODE solver-dependent methods like conditional flow matching (CFM). We demonstrate CaLMFlow's effectiveness on synthetic and real-world data, including single-cell perturbation response prediction, showcasing its ability to incorporate textual context and generalize to unseen conditions. Our results highlight LLM-driven flow matching as a promising paradigm in generative modeling, offering improved scalability, flexibility, and context-awareness.

Flow Matching (FM) is a recent framework for generative modeling that has achieved state-of-the-art performance across various domains, including image, video, audio, speech, and biological structures. This guide offers a comprehensive and self-contained review of FM, covering its mathematical foundations, design choices, and extensions. By also providing a PyTorch package featuring relevant examples (e.g., image and text generation), this work aims to serve as a resource for both novice and experienced researchers interested in understanding, applying and further developing FM.

Continuous normalizing flows (CNFs) learn an ordinary differential equation to transform prior samples into data. Flow matching (FM) has recently emerged as a simulation-free approach for training CNFs by regressing a velocity model towards the conditional velocity field. However, on constrained domains, the learned velocity model may lead to undesirable flows that result in highly unnatural samples, e.g., oversaturated images, due to both flow matching error and simulation error. To address this, we add a boundary constraint term to CNFs, which leads to reflected CNFs that keep trajectories within the constrained domains. We propose reflected flow matching (RFM) to train the velocity model in reflected CNFs by matching the conditional velocity fields in a simulation-free manner, similar to the vanilla FM. Moreover, the analytical form of conditional velocity fields in RFM avoids potentially biased approximations, making it superior to existing score-based generative models on constrained domains. We demonstrate that RFM achieves comparable or better results on standard image benchmarks and produces high-quality class-conditioned samples under high guidance weight.

Diffusion models have achieved significant progress in both image and video generation while still suffering from huge computation costs. As an effective solution, flow matching aims to reflow the diffusion process of diffusion models into a straight line for a few-step and even one-step generation. However, in this paper, we suggest that the original training pipeline of flow matching is not optimal and introduce two techniques to improve it. Firstly, we introduce progressive reflow, which progressively reflows the diffusion models in local timesteps until the whole diffusion progresses, reducing the difficulty of flow matching. Second, we introduce aligned v-prediction, which highlights the importance of direction matching in flow matching over magnitude matching. Experimental results on SDv1.5 and SDXL demonstrate the effectiveness of our method, for example, conducting on SDv1.5 achieves an FID of 10.70 on MSCOCO2014 validation set with only 4 sampling steps, close to our teacher model (32 DDIM steps, FID = 10.05).

Discrete diffusion or flow models could enable faster and more controllable sequence generation than autoregressive models. We show that na\"ive linear flow matching on the simplex is insufficient toward this goal since it suffers from discontinuities in the training target and further pathologies. To overcome this, we develop Dirichlet flow matching on the simplex based on mixtures of Dirichlet distributions as probability paths. In this framework, we derive a connection between the mixtures' scores and the flow's vector field that allows for classifier and classifier-free guidance. Further, we provide distilled Dirichlet flow matching, which enables one-step sequence generation with minimal performance hits, resulting in O(L) speedups compared to autoregressive models. On complex DNA sequence generation tasks, we demonstrate superior performance compared to all baselines in distributional metrics and in achieving desired design targets for generated sequences. Finally, we show that our classifier-free guidance approach improves unconditional generation and is effective for generating DNA that satisfies design targets. Code is available at https://github.com/HannesStark/dirichlet-flow-matching.

This paper presents a novel framework for aligning learnable latent spaces to arbitrary target distributions by leveraging flow-based generative models as priors. Our method first pretrains a flow model on the target features to capture the underlying distribution. This fixed flow model subsequently regularizes the latent space via an alignment loss, which reformulates the flow matching objective to treat the latents as optimization targets. We formally prove that minimizing this alignment loss establishes a computationally tractable surrogate objective for maximizing a variational lower bound on the log-likelihood of latents under the target distribution. Notably, the proposed method eliminates computationally expensive likelihood evaluations and avoids ODE solving during optimization. As a proof of concept, we demonstrate in a controlled setting that the alignment loss landscape closely approximates the negative log-likelihood of the target distribution. We further validate the effectiveness of our approach through large-scale image generation experiments on ImageNet with diverse target distributions, accompanied by detailed discussions and ablation studies. With both theoretical and empirical validation, our framework paves a new way for latent space alignment.

We present a formulation of flow matching as variational inference, which we refer to as variational flow matching (VFM). Based on this formulation we develop CatFlow, a flow matching method for categorical data. CatFlow is easy to implement, computationally efficient, and achieves strong results on graph generation tasks. In VFM, the objective is to approximate the posterior probability path, which is a distribution over possible end points of a trajectory. We show that VFM admits both the CatFlow objective and the original flow matching objective as special cases. We also relate VFM to score-based models, in which the dynamics are stochastic rather than deterministic, and derive a bound on the model likelihood based on a reweighted VFM objective. We evaluate CatFlow on one abstract graph generation task and two molecular generation tasks. In all cases, CatFlow exceeds or matches performance of the current state-of-the-art models.

Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although inverse problem solving has been extensively explored using diffusion models, it has not been rigorously examined within the broader context of flow models. Therefore, here we extend the diffusion inverse solvers (DIS) - which perform posterior sampling by combining a denoising diffusion prior with an likelihood gradient - into the flow framework. Specifically, by driving the flow-version of Tweedie's formula, we decompose the flow ODE into two components: one for clean image estimation and the other for noise estimation. By integrating the likelihood gradient and stochastic noise into each component, respectively, we demonstrate that posterior sampling for inverse problem solving can be effectively achieved using flows. Our proposed solver, Flow-Driven Posterior Sampling (FlowDPS), can also be seamlessly integrated into a latent flow model with a transformer architecture. Across four linear inverse problems, we confirm that FlowDPS outperforms state-of-the-art alternatives, all without requiring additional training.

Flow Matching has emerged as a powerful framework for learning continuous transformations between distributions, enabling high-fidelity generative modeling. This work introduces Symmetrical Flow Matching (SymmFlow), a new formulation that unifies semantic segmentation, classification, and image generation within a single model. Using a symmetric learning objective, SymmFlow models forward and reverse transformations jointly, ensuring bi-directional consistency, while preserving sufficient entropy for generative diversity. A new training objective is introduced to explicitly retain semantic information across flows, featuring efficient sampling while preserving semantic structure, allowing for one-step segmentation and classification without iterative refinement. Unlike previous approaches that impose strict one-to-one mapping between masks and images, SymmFlow generalizes to flexible conditioning, supporting both pixel-level and image-level class labels. Experimental results on various benchmarks demonstrate that SymmFlow achieves state-of-the-art performance on semantic image synthesis, obtaining FID scores of 11.9 on CelebAMask-HQ and 7.0 on COCO-Stuff with only 25 inference steps. Additionally, it delivers competitive results on semantic segmentation and shows promising capabilities in classification tasks. The code will be publicly available.

The multi-step denoising process in diffusion and Flow Matching models causes major efficiency issues, which motivates research on few-step generation. We present Solution Flow Models (SoFlow), a framework for one-step generation from scratch. By analyzing the relationship between the velocity function and the solution function of the velocity ordinary differential equation (ODE), we propose a Flow Matching loss and a solution consistency loss to train our models. The Flow Matching loss allows our models to provide estimated velocity fields for Classifier-Free Guidance (CFG) during training, which improves generation performance. Notably, our consistency loss does not require the calculation of the Jacobian-vector product (JVP), a common requirement in recent works that is not well-optimized in deep learning frameworks like PyTorch. Experimental results indicate that, when trained from scratch using the same Diffusion Transformer (DiT) architecture and an equal number of training epochs, our models achieve better FID-50K scores than MeanFlow models on the ImageNet 256x256 dataset.

MeanFlow has recently emerged as a powerful framework for few-step generative modeling trained from scratch, but its success is not yet fully understood. In this work, we show that the MeanFlow objective naturally decomposes into two parts: trajectory flow matching and trajectory consistency. Through gradient analysis, we find that these terms are strongly negatively correlated, causing optimization conflict and slow convergence. Motivated by these insights, we introduce alpha-Flow, a broad family of objectives that unifies trajectory flow matching, Shortcut Model, and MeanFlow under one formulation. By adopting a curriculum strategy that smoothly anneals from trajectory flow matching to MeanFlow, alpha-Flow disentangles the conflicting objectives, and achieves better convergence. When trained from scratch on class-conditional ImageNet-1K 256x256 with vanilla DiT backbones, alpha-Flow consistently outperforms MeanFlow across scales and settings. Our largest alpha-Flow-XL/2+ model achieves new state-of-the-art results using vanilla DiT backbones, with FID scores of 2.58 (1-NFE) and 2.15 (2-NFE).

Recent advances in generative modeling have demonstrated strong promise for high-quality point cloud upsampling. In this work, we present PUFM++, an enhanced flow-matching framework for reconstructing dense and accurate point clouds from sparse, noisy, and partial observations. PUFM++ improves flow matching along three key axes: (i) geometric fidelity, (ii) robustness to imperfect input, and (iii) consistency with downstream surface-based tasks. We introduce a two-stage flow-matching strategy that first learns a direct, straight-path flow from sparse inputs to dense targets, and then refines it using noise-perturbed samples to approximate the terminal marginal distribution better. To accelerate and stabilize inference, we propose a data-driven adaptive time scheduler that improves sampling efficiency based on interpolation behavior. We further impose on-manifold constraints during sampling to ensure that generated points remain aligned with the underlying surface. Finally, we incorporate a recurrent interface network~(RIN) to strengthen hierarchical feature interactions and boost reconstruction quality. Extensive experiments on synthetic benchmarks and real-world scans show that PUFM++ sets a new state of the art in point cloud upsampling, delivering superior visual fidelity and quantitative accuracy across a wide range of tasks. Code and pretrained models are publicly available at https://github.com/Holmes-Alan/Enhanced_PUFM.

We present an ultra-efficient post-training method for shortcutting large-scale pre-trained flow matching diffusion models into efficient few-step samplers, enabled by novel velocity field self-distillation. While shortcutting in flow matching, originally introduced by shortcut models, offers flexible trajectory-skipping capabilities, it requires a specialized step-size embedding incompatible with existing models unless retraining from scratchx2013a process nearly as costly as pretraining itself. Our key contribution is thus imparting a more aggressive shortcut mechanism to standard flow matching models (e.g., Flux), leveraging a unique distillation principle that obviates the need for step-size embedding. Working on the velocity field rather than sample space and learning rapidly from self-guided distillation in an online manner, our approach trains efficiently, e.g., producing a 3-step Flux less than one A100 day. Beyond distillation, our method can be incorporated into the pretraining stage itself, yielding models that inherently learn efficient, few-step flows without compromising quality. This capability also enables, to our knowledge, the first few-shot distillation method (e.g., 10 text-image pairs) for dozen-billion-parameter diffusion models, delivering state-of-the-art performance at almost free cost.

Scene flow estimation is a long-standing problem in computer vision, where the goal is to find the 3D motion of a scene from its consecutive observations. Recently, there have been efforts to compute the scene flow from 3D point clouds. A common approach is to train a regression model that consumes source and target point clouds and outputs the per-point translation vector. An alternative is to learn point matches between the point clouds concurrently with regressing a refinement of the initial correspondence flow. In both cases, the learning task is very challenging since the flow regression is done in the free 3D space, and a typical solution is to resort to a large annotated synthetic dataset. We introduce SCOOP, a new method for scene flow estimation that can be learned on a small amount of data without employing ground-truth flow supervision. In contrast to previous work, we train a pure correspondence model focused on learning point feature representation and initialize the flow as the difference between a source point and its softly corresponding target point. Then, in the run-time phase, we directly optimize a flow refinement component with a self-supervised objective, which leads to a coherent and accurate flow field between the point clouds. Experiments on widespread datasets demonstrate the performance gains achieved by our method compared to existing leading techniques while using a fraction of the training data. Our code is publicly available at https://github.com/itailang/SCOOP.

Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each data sample. However, these algorithms rely on independent data and noise samples, and do not exploit underlying structure in the data distribution for constructing probability paths. We propose Multisample Flow Matching, a more general framework that uses non-trivial couplings between data and noise samples while satisfying the correct marginal constraints. At very small overhead costs, this generalization allows us to (i) reduce gradient variance during training, (ii) obtain straighter flows for the learned vector field, which allows us to generate high-quality samples using fewer function evaluations, and (iii) obtain transport maps with lower cost in high dimensions, which has applications beyond generative modeling. Importantly, we do so in a completely simulation-free manner with a simple minimization objective. We show that our proposed methods improve sample consistency on downsampled ImageNet data sets, and lead to better low-cost sample generation.

Flow-based generative models are powerful exact likelihood models with efficient sampling and inference. Despite their computational efficiency, flow-based models generally have much worse density modeling performance compared to state-of-the-art autoregressive models. In this paper, we investigate and improve upon three limiting design choices employed by flow-based models in prior work: the use of uniform noise for dequantization, the use of inexpressive affine flows, and the use of purely convolutional conditioning networks in coupling layers. Based on our findings, we propose Flow++, a new flow-based model that is now the state-of-the-art non-autoregressive model for unconditional density estimation on standard image benchmarks. Our work has begun to close the significant performance gap that has so far existed between autoregressive models and flow-based models. Our implementation is available at https://github.com/aravindsrinivas/flowpp

We propose a flow-guided transformer, which innovatively leverage the motion discrepancy exposed by optical flows to instruct the attention retrieval in transformer for high fidelity video inpainting. More specially, we design a novel flow completion network to complete the corrupted flows by exploiting the relevant flow features in a local temporal window. With the completed flows, we propagate the content across video frames, and adopt the flow-guided transformer to synthesize the rest corrupted regions. We decouple transformers along temporal and spatial dimension, so that we can easily integrate the locally relevant completed flows to instruct spatial attention only. Furthermore, we design a flow-reweight module to precisely control the impact of completed flows on each spatial transformer. For the sake of efficiency, we introduce window partition strategy to both spatial and temporal transformers. Especially in spatial transformer, we design a dual perspective spatial MHSA, which integrates the global tokens to the window-based attention. Extensive experiments demonstrate the effectiveness of the proposed method qualitatively and quantitatively. Codes are available at https://github.com/hitachinsk/FGT.

Conditional generative modeling aims to learn a conditional data distribution from samples containing data-condition pairs. For this, diffusion and flow-based methods have attained compelling results. These methods use a learned (flow) model to transport an initial standard Gaussian noise that ignores the condition to the conditional data distribution. The model is hence required to learn both mass transport and conditional injection. To ease the demand on the model, we propose Condition-Aware Reparameterization for Flow Matching (CAR-Flow) -- a lightweight, learned shift that conditions the source, the target, or both distributions. By relocating these distributions, CAR-Flow shortens the probability path the model must learn, leading to faster training in practice. On low-dimensional synthetic data, we visualize and quantify the effects of CAR. On higher-dimensional natural image data (ImageNet-256), equipping SiT-XL/2 with CAR-Flow reduces FID from 2.07 to 1.68, while introducing less than 0.6% additional parameters.

Recent advancements in flow-matching have enabled high-quality text-to-image generation. However, the deterministic nature of flow-matching models makes them poorly suited for reinforcement learning, a key tool for improving image quality and human alignment. Prior work has introduced stochasticity by perturbing latents with random noise, but such perturbations are inefficient and unstable. We propose Smart-GRPO, the first method to optimize noise perturbations for reinforcement learning in flow-matching models. Smart-GRPO employs an iterative search strategy that decodes candidate perturbations, evaluates them with a reward function, and refines the noise distribution toward higher-reward regions. Experiments demonstrate that Smart-GRPO improves both reward optimization and visual quality compared to baseline methods. Our results suggest a practical path toward reinforcement learning in flow-matching frameworks, bridging the gap between efficient training and human-aligned generation.

Finding a suitable layout represents a crucial task for diverse applications in graphic design. Motivated by simpler and smoother sampling trajectories, we explore the use of Flow Matching as an alternative to current diffusion-based layout generation models. Specifically, we propose LayoutFlow, an efficient flow-based model capable of generating high-quality layouts. Instead of progressively denoising the elements of a noisy layout, our method learns to gradually move, or flow, the elements of an initial sample until it reaches its final prediction. In addition, we employ a conditioning scheme that allows us to handle various generation tasks with varying degrees of conditioning with a single model. Empirically, LayoutFlow performs on par with state-of-the-art models while being significantly faster.

Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this work, we present Discrete Flow Matching, a novel discrete flow paradigm designed specifically for generating discrete data. Discrete Flow Matching offers several key contributions: (i) it works with a general family of probability paths interpolating between source and target distributions; (ii) it allows for a generic formula for sampling from these probability paths using learned posteriors such as the probability denoiser (x-prediction) and noise-prediction (epsilon-prediction); (iii) practically, focusing on specific probability paths defined with different schedulers considerably improves generative perplexity compared to previous discrete diffusion and flow models; and (iv) by scaling Discrete Flow Matching models up to 1.7B parameters, we reach 6.7% Pass@1 and 13.4% Pass@10 on HumanEval and 6.7% Pass@1 and 20.6% Pass@10 on 1-shot MBPP coding benchmarks. Our approach is capable of generating high-quality discrete data in a non-autoregressive fashion, significantly closing the gap between autoregressive models and discrete flow models.

Rectified flow models have become a de facto standard in image generation due to their stable sampling trajectories and high-fidelity outputs. Despite their strong generative capabilities, they face critical limitations in image editing tasks: inaccurate inversion processes for mapping real images back into the latent space, and gradient entanglement issues during editing often result in outputs that do not faithfully reflect the target prompt. Recent efforts have attempted to directly map source and target distributions via ODE-based approaches without inversion; however,these methods still yield suboptimal editing quality. In this work, we propose a flow decomposition-and-aggregation framework built upon an inversion-free formulation to address these limitations. Specifically, we semantically decompose the target prompt into multiple sub-prompts, compute an independent flow for each, and aggregate them to form a unified editing trajectory. While we empirically observe that decomposing the original flow enhances diversity in the target space, generating semantically aligned outputs still requires consistent guidance toward the full target prompt. To this end, we design a projection and soft-aggregation mechanism for flow, inspired by gradient conflict resolution in multi-task learning. This approach adaptively weights the sub-target velocity fields, suppressing semantic redundancy while emphasizing distinct directions, thereby preserving both diversity and consistency in the final edited output. Experimental results demonstrate that our method outperforms existing zero-shot editing approaches in terms of semantic fidelity and attribute disentanglement. The code is available at https://github.com/Harvard-AI-and-Robotics-Lab/SplitFlow.

Editing real images using a pre-trained text-to-image (T2I) diffusion/flow model often involves inverting the image into its corresponding noise map. However, inversion by itself is typically insufficient for obtaining satisfactory results, and therefore many methods additionally intervene in the sampling process. Such methods achieve improved results but are not seamlessly transferable between model architectures. Here, we introduce FlowEdit, a text-based editing method for pre-trained T2I flow models, which is inversion-free, optimization-free and model agnostic. Our method constructs an ODE that directly maps between the source and target distributions (corresponding to the source and target text prompts) and achieves a lower transport cost than the inversion approach. This leads to state-of-the-art results, as we illustrate with Stable Diffusion 3 and FLUX. Code and examples are available on the project's webpage.

We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently unable to scale to high dimensions, or use approximations for limiting quantities that result in biased training objectives. Riemannian Flow Matching bypasses these limitations and offers several advantages over previous approaches: it is simulation-free on simple geometries, does not require divergence computation, and computes its target vector field in closed-form. The key ingredient behind RFM is the construction of a relatively simple premetric for defining target vector fields, which encompasses the existing Euclidean case. To extend to general geometries, we rely on the use of spectral decompositions to efficiently compute premetrics on the fly. Our method achieves state-of-the-art performance on many real-world non-Euclidean datasets, and we demonstrate tractable training on general geometries, including triangular meshes with highly non-trivial curvature and boundaries.

Explicitly disentangling style and content in vision models remains challenging due to their semantic overlap and the subjectivity of human perception. Existing methods propose separation through generative or discriminative objectives, but they still face the inherent ambiguity of disentangling intertwined concepts. Instead, we ask: Can we bypass explicit disentanglement by learning to merge style and content invertibly, allowing separation to emerge naturally? We propose SCFlow, a flow-matching framework that learns bidirectional mappings between entangled and disentangled representations. Our approach is built upon three key insights: 1) Training solely to merge style and content, a well-defined task, enables invertible disentanglement without explicit supervision; 2) flow matching bridges on arbitrary distributions, avoiding the restrictive Gaussian priors of diffusion models and normalizing flows; and 3) a synthetic dataset of 510,000 samples (51 styles times 10,000 content samples) was curated to simulate disentanglement through systematic style-content pairing. Beyond controllable generation tasks, we demonstrate that SCFlow generalizes to ImageNet-1k and WikiArt in zero-shot settings and achieves competitive performance, highlighting that disentanglement naturally emerges from the invertible merging process.

Continuous-time Consistency Models (CMs) promise efficient few-step generation but face significant challenges with training instability. We argue this instability stems from a fundamental conflict: by training a network to learn only a shortcut across a probability flow, the model loses its grasp on the instantaneous velocity field that defines the flow. Our solution is to explicitly anchor the model in the underlying flow during training. We introduce the Flow-Anchored Consistency Model (FACM), a simple but effective training strategy that uses a Flow Matching (FM) task as an anchor for the primary CM shortcut objective. This Flow-Anchoring approach requires no architectural modifications and is broadly compatible with standard model architectures. By distilling a pre-trained LightningDiT model, our method achieves a state-of-the-art FID of 1.32 with two steps (NFE=2) and 1.76 with just one step (NFE=1) on ImageNet 256x256, significantly outperforming previous methods. This provides a general and effective recipe for building high-performance, few-step generative models. Our code and pretrained models: https://github.com/ali-vilab/FACM.

Advanced generative models excel at synthesizing images but often rely on text-based conditioning. Visual designers, however, often work beyond language, directly drawing inspiration from existing visual elements. In many cases, these elements represent only fragments of a potential concept-such as an uniquely structured wing, or a specific hairstyle-serving as inspiration for the artist to explore how they can come together creatively into a coherent whole. Recognizing this need, we introduce a generative framework that seamlessly integrates a partial set of user-provided visual components into a coherent composition while simultaneously sampling the missing parts needed to generate a plausible and complete concept. Our approach builds on a strong and underexplored representation space, extracted from IP-Adapter+, on which we train IP-Prior, a lightweight flow-matching model that synthesizes coherent compositions based on domain-specific priors, enabling diverse and context-aware generations. Additionally, we present a LoRA-based fine-tuning strategy that significantly improves prompt adherence in IP-Adapter+ for a given task, addressing its common trade-off between reconstruction quality and prompt adherence.

Diffusion- and flow-based models have emerged as state-of-the-art generative modeling approaches, but they require many sampling steps. Consistency models can distill these models into efficient one-step generators; however, unlike flow- and diffusion-based methods, their performance inevitably degrades when increasing the number of steps, which we show both analytically and empirically. Flow maps generalize these approaches by connecting any two noise levels in a single step and remain effective across all step counts. In this paper, we introduce two new continuous-time objectives for training flow maps, along with additional novel training techniques, generalizing existing consistency and flow matching objectives. We further demonstrate that autoguidance can improve performance, using a low-quality model for guidance during distillation, and an additional boost can be achieved by adversarial finetuning, with minimal loss in sample diversity. We extensively validate our flow map models, called Align Your Flow, on challenging image generation benchmarks and achieve state-of-the-art few-step generation performance on both ImageNet 64x64 and 512x512, using small and efficient neural networks. Finally, we show text-to-image flow map models that outperform all existing non-adversarially trained few-step samplers in text-conditioned synthesis.

The practical use of text-to-image generation has evolved from simple, monolithic models to complex workflows that combine multiple specialized components. While workflow-based approaches can lead to improved image quality, crafting effective workflows requires significant expertise, owing to the large number of available components, their complex inter-dependence, and their dependence on the generation prompt. Here, we introduce the novel task of prompt-adaptive workflow generation, where the goal is to automatically tailor a workflow to each user prompt. We propose two LLM-based approaches to tackle this task: a tuning-based method that learns from user-preference data, and a training-free method that uses the LLM to select existing flows. Both approaches lead to improved image quality when compared to monolithic models or generic, prompt-independent workflows. Our work shows that prompt-dependent flow prediction offers a new pathway to improving text-to-image generation quality, complementing existing research directions in the field.

The remarkable success of diffusion and flow-matching models has ignited a surge of works on adapting them at test time for controlled generation tasks. Examples range from image editing to restoration, compression and personalization. However, due to the iterative nature of the sampling process in those models, it is computationally impractical to use gradient-based optimization to directly control the image generated at the end of the process. As a result, existing methods typically resort to manipulating each timestep separately. Here we introduce FlowOpt - a zero-order (gradient-free) optimization framework that treats the entire flow process as a black box, enabling optimization through the whole sampling path without backpropagation through the model. Our method is both highly efficient and allows users to monitor the intermediate optimization results and perform early stopping if desired. We prove a sufficient condition on FlowOpt's step-size, under which convergence to the global optimum is guaranteed. We further show how to empirically estimate this upper bound so as to choose an appropriate step-size. We demonstrate how FlowOpt can be used for image editing, showcasing two options: (i) inversion (determining the initial noise that generates a given image), and (ii) directly steering the edited image to be similar to the source image while conforming to a target text prompt. In both cases, FlowOpt achieves state-of-the-art results while using roughly the same number of neural function evaluations (NFEs) as existing methods. Code and examples are available on the project's webpage.

State-of-the-art flow models achieve remarkable quality but require slow, iterative sampling. To accelerate this, flow maps can be distilled from pre-trained teachers, a procedure that conventionally requires sampling from an external dataset. We argue that this data-dependency introduces a fundamental risk of Teacher-Data Mismatch, as a static dataset may provide an incomplete or even misaligned representation of the teacher's full generative capabilities. This leads us to question whether this reliance on data is truly necessary for successful flow map distillation. In this work, we explore a data-free alternative that samples only from the prior distribution, a distribution the teacher is guaranteed to follow by construction, thereby circumventing the mismatch risk entirely. To demonstrate the practical viability of this philosophy, we introduce a principled framework that learns to predict the teacher's sampling path while actively correcting for its own compounding errors to ensure high fidelity. Our approach surpasses all data-based counterparts and establishes a new state-of-the-art by a significant margin. Specifically, distilling from SiT-XL/2+REPA, our method reaches an impressive FID of 1.45 on ImageNet 256x256, and 1.49 on ImageNet 512x512, both with only 1 sampling step. We hope our work establishes a more robust paradigm for accelerating generative models and motivates the broader adoption of flow map distillation without data.

Diffusion models approximate the denoising distribution as a Gaussian and predict its mean, whereas flow matching models reparameterize the Gaussian mean as flow velocity. However, they underperform in few-step sampling due to discretization error and tend to produce over-saturated colors under classifier-free guidance (CFG). To address these limitations, we propose a novel Gaussian mixture flow matching (GMFlow) model: instead of predicting the mean, GMFlow predicts dynamic Gaussian mixture (GM) parameters to capture a multi-modal flow velocity distribution, which can be learned with a KL divergence loss. We demonstrate that GMFlow generalizes previous diffusion and flow matching models where a single Gaussian is learned with an L_2 denoising loss. For inference, we derive GM-SDE/ODE solvers that leverage analytic denoising distributions and velocity fields for precise few-step sampling. Furthermore, we introduce a novel probabilistic guidance scheme that mitigates the over-saturation issues of CFG and improves image generation quality. Extensive experiments demonstrate that GMFlow consistently outperforms flow matching baselines in generation quality, achieving a Precision of 0.942 with only 6 sampling steps on ImageNet 256times256.

State-of-the-art text-to-image models produce visually impressive results but often struggle with precise alignment to text prompts, leading to missing critical elements or unintended blending of distinct concepts. We propose a novel approach that learns a high-success-rate distribution conditioned on a target prompt, ensuring that generated images faithfully reflect the corresponding prompts. Our method explicitly models the signal component during the denoising process, offering fine-grained control that mitigates over-optimization and out-of-distribution artifacts. Moreover, our framework is training-free and seamlessly integrates with both existing diffusion and flow matching architectures. It also supports additional conditioning modalities -- such as bounding boxes -- for enhanced spatial alignment. Extensive experiments demonstrate that our approach outperforms current state-of-the-art methods. The code is available at https://github.com/grimalPaul/gsn-factory.

Flow Matching (FM) algorithm achieves remarkable results in generative tasks especially in robotic manipulation. Building upon the foundations of diffusion models, the simulation-free paradigm of FM enables simple and efficient training, but inherently introduces a train-inference gap. Specifically, we cannot assess the model's output during the training phase. In contrast, other generative models including Variational Autoencoder (VAE), Normalizing Flow and Generative Adversarial Networks (GANs) directly optimize on the reconstruction loss. Such a gap is particularly evident in scenarios that demand high precision, such as robotic manipulation. Moreover, we show that FM's over-pursuit of straight predefined paths may introduce some serious problems such as stiffness into the system. These motivate us to fine-tune FM via Maximum Likelihood Estimation of reconstructions - an approach made feasible by FM's underlying smooth ODE formulation, in contrast to the stochastic differential equations (SDEs) used in diffusion models. This paper first theoretically analyzes the relation between training loss and inference error in FM. Then we propose a method of fine-tuning FM via Maximum Likelihood Estimation of reconstructions, which includes both straightforward fine-tuning and residual-based fine-tuning approaches. Furthermore, through specifically designed architectures, the residual-based fine-tuning can incorporate the contraction property into the model, which is crucial for the model's robustness and interpretability. Experimental results in image generation and robotic manipulation verify that our method reliably improves the inference performance of FM.

Learning to localize the sound source in videos without explicit annotations is a novel area of audio-visual research. Existing work in this area focuses on creating attention maps to capture the correlation between the two modalities to localize the source of the sound. In a video, oftentimes, the objects exhibiting movement are the ones generating the sound. In this work, we capture this characteristic by modeling the optical flow in a video as a prior to better aid in localizing the sound source. We further demonstrate that the addition of flow-based attention substantially improves visual sound source localization. Finally, we benchmark our method on standard sound source localization datasets and achieve state-of-the-art performance on the Soundnet Flickr and VGG Sound Source datasets. Code: https://github.com/denfed/heartheflow.

Classifier-Free Guidance (CFG) is a widely adopted technique in diffusion/flow models to improve image fidelity and controllability. In this work, we first analytically study the effect of CFG on flow matching models trained on Gaussian mixtures where the ground-truth flow can be derived. We observe that in the early stages of training, when the flow estimation is inaccurate, CFG directs samples toward incorrect trajectories. Building on this observation, we propose CFG-Zero*, an improved CFG with two contributions: (a) optimized scale, where a scalar is optimized to correct for the inaccuracies in the estimated velocity, hence the * in the name; and (b) zero-init, which involves zeroing out the first few steps of the ODE solver. Experiments on both text-to-image (Lumina-Next, Stable Diffusion 3, and Flux) and text-to-video (Wan-2.1) generation demonstrate that CFG-Zero* consistently outperforms CFG, highlighting its effectiveness in guiding Flow Matching models. (Code is available at github.com/WeichenFan/CFG-Zero-star)

Learning-based optical flow estimation has been dominated with the pipeline of cost volume with convolutions for flow regression, which is inherently limited to local correlations and thus is hard to address the long-standing challenge of large displacements. To alleviate this, the state-of-the-art framework RAFT gradually improves its prediction quality by using a large number of iterative refinements, achieving remarkable performance but introducing linearly increasing inference time. To enable both high accuracy and efficiency, we completely revamp the dominant flow regression pipeline by reformulating optical flow as a global matching problem, which identifies the correspondences by directly comparing feature similarities. Specifically, we propose a GMFlow framework, which consists of three main components: a customized Transformer for feature enhancement, a correlation and softmax layer for global feature matching, and a self-attention layer for flow propagation. We further introduce a refinement step that reuses GMFlow at higher feature resolution for residual flow prediction. Our new framework outperforms 31-refinements RAFT on the challenging Sintel benchmark, while using only one refinement and running faster, suggesting a new paradigm for accurate and efficient optical flow estimation. Code is available at https://github.com/haofeixu/gmflow.

Normalizing Flows explicitly maximize a full-dimensional likelihood on the training data. However, real data is typically only supported on a lower-dimensional manifold leading the model to expend significant compute on modeling noise. Injective Flows fix this by jointly learning a manifold and the distribution on it. So far, they have been limited by restrictive architectures and/or high computational cost. We lift both constraints by a new efficient estimator for the maximum likelihood loss, compatible with free-form bottleneck architectures. We further show that naively learning both the data manifold and the distribution on it can lead to divergent solutions, and use this insight to motivate a stable maximum likelihood training objective. We perform extensive experiments on toy, tabular and image data, demonstrating the competitive performance of the resulting model.

Normalizing Flows (NFs) have been established as a principled framework for generative modeling. Standard NFs consist of a forward process and a reverse process: the forward process maps data to noise, while the reverse process generates samples by inverting it. Typical NF forward transformations are constrained by explicit invertibility, ensuring that the reverse process can serve as their exact analytic inverse. Recent developments in TARFlow and its variants have revitalized NF methods by combining Transformers and autoregressive flows, but have also exposed causal decoding as a major bottleneck. In this work, we introduce Bidirectional Normalizing Flow (BiFlow), a framework that removes the need for an exact analytic inverse. BiFlow learns a reverse model that approximates the underlying noise-to-data inverse mapping, enabling more flexible loss functions and architectures. Experiments on ImageNet demonstrate that BiFlow, compared to its causal decoding counterpart, improves generation quality while accelerating sampling by up to two orders of magnitude. BiFlow yields state-of-the-art results among NF-based methods and competitive performance among single-evaluation ("1-NFE") methods. Following recent encouraging progress on NFs, we hope our work will draw further attention to this classical paradigm.

Transformers were originally proposed as a sequence-to-sequence model for text but have become vital for a wide range of modalities, including images, audio, video, and undirected graphs. However, transformers for directed graphs are a surprisingly underexplored topic, despite their applicability to ubiquitous domains including source code and logic circuits. In this work, we propose two direction- and structure-aware positional encodings for directed graphs: (1) the eigenvectors of the Magnetic Laplacian - a direction-aware generalization of the combinatorial Laplacian; (2) directional random walk encodings. Empirically, we show that the extra directionality information is useful in various downstream tasks, including correctness testing of sorting networks and source code understanding. Together with a data-flow-centric graph construction, our model outperforms the prior state of the art on the Open Graph Benchmark Code2 relatively by 14.7%.

We present JanusFlow, a powerful framework that unifies image understanding and generation in a single model. JanusFlow introduces a minimalist architecture that integrates autoregressive language models with rectified flow, a state-of-the-art method in generative modeling. Our key finding demonstrates that rectified flow can be straightforwardly trained within the large language model framework, eliminating the need for complex architectural modifications. To further improve the performance of our unified model, we adopt two key strategies: (i) decoupling the understanding and generation encoders, and (ii) aligning their representations during unified training. Extensive experiments show that JanusFlow achieves comparable or superior performance to specialized models in their respective domains, while significantly outperforming existing unified approaches across standard benchmarks. This work represents a step toward more efficient and versatile vision-language models.

We present Piecewise Rectified Flow (PeRFlow), a flow-based method for accelerating diffusion models. PeRFlow divides the sampling process of generative flows into several time windows and straightens the trajectories in each interval via the reflow operation, thereby approaching piecewise linear flows. PeRFlow achieves superior performance in a few-step generation. Moreover, through dedicated parameterizations, the obtained PeRFlow models show advantageous transfer ability, serving as universal plug-and-play accelerators that are compatible with various workflows based on the pre-trained diffusion models. The implementations of training and inference are fully open-sourced. https://github.com/magic-research/piecewise-rectified-flow

Recently, there has been tremendous progress in visual synthesis and the underlying generative models. Here, diffusion models (DMs) stand out particularly, but lately, flow matching (FM) has also garnered considerable interest. While DMs excel in providing diverse images, they suffer from long training and slow generation. With latent diffusion, these issues are only partially alleviated. Conversely, FM offers faster training and inference but exhibits less diversity in synthesis. We demonstrate that introducing FM between the Diffusion model and the convolutional decoder offers high-resolution image synthesis with reduced computational cost and model size. Diffusion can then efficiently provide the necessary generation diversity. FM compensates for the lower resolution, mapping the small latent space to a high-dimensional one. Subsequently, the convolutional decoder of the LDM maps these latents to high-resolution images. By combining the diversity of DMs, the efficiency of FMs, and the effectiveness of convolutional decoders, we achieve state-of-the-art high-resolution image synthesis at 1024^2 with minimal computational cost. Importantly, our approach is orthogonal to recent approximation and speed-up strategies for the underlying DMs, making it easily integrable into various DM frameworks.

Training datasets are inherently imperfect, often containing mislabeled samples due to human annotation errors, limitations of tagging models, and other sources of noise. Such label contamination can significantly degrade the performance of a trained model. In this work, we introduce Self-Purifying Flow Matching (SPFM), a principled approach to filtering unreliable data within the flow-matching framework. SPFM identifies suspicious data using the model itself during the training process, bypassing the need for pretrained models or additional modules. Our experiments demonstrate that models trained with SPFM generate samples that accurately adhere to the specified conditioning, even when trained on noisy labels. Furthermore, we validate the robustness of SPFM on the TITW dataset, which consists of in-the-wild speech data, achieving performance that surpasses existing baselines.

While recent flow-based image editing models demonstrate general-purpose capabilities across diverse tasks, they often struggle to specialize in challenging scenarios -- particularly those involving large-scale shape transformations. When performing such structural edits, these methods either fail to achieve the intended shape change or inadvertently alter non-target regions, resulting in degraded background quality. We propose Follow-Your-Shape, a training-free and mask-free framework that supports precise and controllable editing of object shapes while strictly preserving non-target content. Motivated by the divergence between inversion and editing trajectories, we compute a Trajectory Divergence Map (TDM) by comparing token-wise velocity differences between the inversion and denoising paths. The TDM enables precise localization of editable regions and guides a Scheduled KV Injection mechanism that ensures stable and faithful editing. To facilitate a rigorous evaluation, we introduce ReShapeBench, a new benchmark comprising 120 new images and enriched prompt pairs specifically curated for shape-aware editing. Experiments demonstrate that our method achieves superior editability and visual fidelity, particularly in tasks requiring large-scale shape replacement.

Generative Flow Networks (GFlowNets) are amortized sampling methods that learn a distribution over discrete objects proportional to their rewards. GFlowNets exhibit a remarkable ability to generate diverse samples, yet occasionally struggle to consistently produce samples with high rewards due to over-exploration on wide sample space. This paper proposes to train GFlowNets with local search, which focuses on exploiting high-rewarded sample space to resolve this issue. Our main idea is to explore the local neighborhood via backtracking and reconstruction guided by backward and forward policies, respectively. This allows biasing the samples toward high-reward solutions, which is not possible for a typical GFlowNet solution generation scheme, which uses the forward policy to generate the solution from scratch. Extensive experiments demonstrate a remarkable performance improvement in several biochemical tasks. Source code is available: https://github.com/dbsxodud-11/ls_gfn.

Taming the generation outcome of state of the art Diffusion and Flow-Matching (FM) models without having to re-train a task-specific model unlocks a powerful tool for solving inverse problems, conditional generation, and controlled generation in general. In this work we introduce D-Flow, a simple framework for controlling the generation process by differentiating through the flow, optimizing for the source (noise) point. We motivate this framework by our key observation stating that for Diffusion/FM models trained with Gaussian probability paths, differentiating through the generation process projects gradient on the data manifold, implicitly injecting the prior into the optimization process. We validate our framework on linear and non-linear controlled generation problems including: image and audio inverse problems and conditional molecule generation reaching state of the art performance across all.

Recent work has shown that leveraging learned predictions can improve the running time of algorithms for bipartite matching and similar combinatorial problems. In this work, we build on this idea to improve the performance of the widely used Ford-Fulkerson algorithm for computing maximum flows by seeding Ford-Fulkerson with predicted flows. Our proposed method offers strong theoretical performance in terms of the quality of the prediction. We then consider image segmentation, a common use-case of flows in computer vision, and complement our theoretical analysis with strong empirical results.

Generative models like Flow Matching have achieved state-of-the-art performance but are often hindered by a computationally expensive iterative sampling process. To address this, recent work has focused on few-step or one-step generation by learning the average velocity field, which directly maps noise to data. MeanFlow, a leading method in this area, learns this field by enforcing a differential identity that connects the average and instantaneous velocities. In this work, we argue that this differential formulation is a limiting special case of a more fundamental principle. We return to the first principles of average velocity and leverage the additivity property of definite integrals. This leads us to derive a novel, purely algebraic identity we term Interval Splitting Consistency. This identity establishes a self-referential relationship for the average velocity field across different time intervals without resorting to any differential operators. Based on this principle, we introduce SplitMeanFlow, a new training framework that enforces this algebraic consistency directly as a learning objective. We formally prove that the differential identity at the core of MeanFlow is recovered by taking the limit of our algebraic consistency as the interval split becomes infinitesimal. This establishes SplitMeanFlow as a direct and more general foundation for learning average velocity fields. From a practical standpoint, our algebraic approach is significantly more efficient, as it eliminates the need for JVP computations, resulting in simpler implementation, more stable training, and broader hardware compatibility. One-step and two-step SplitMeanFlow models have been successfully deployed in large-scale speech synthesis products (such as Doubao), achieving speedups of 20x.

Language-queried audio source separation (LASS) focuses on separating sounds using textual descriptions of the desired sources. Current methods mainly use discriminative approaches, such as time-frequency masking, to separate target sounds and minimize interference from other sources. However, these models face challenges when separating overlapping soundtracks, which may lead to artifacts such as spectral holes or incomplete separation. Rectified flow matching (RFM), a generative model that establishes linear relations between the distribution of data and noise, offers superior theoretical properties and simplicity, but has not yet been explored in sound separation. In this work, we introduce FlowSep, a new generative model based on RFM for LASS tasks. FlowSep learns linear flow trajectories from noise to target source features within the variational autoencoder (VAE) latent space. During inference, the RFM-generated latent features are reconstructed into a mel-spectrogram via the pre-trained VAE decoder, followed by a pre-trained vocoder to synthesize the waveform. Trained on 1,680 hours of audio data, FlowSep outperforms the state-of-the-art models across multiple benchmarks, as evaluated with subjective and objective metrics. Additionally, our results show that FlowSep surpasses a diffusion-based LASS model in both separation quality and inference efficiency, highlighting its strong potential for audio source separation tasks. Code, pre-trained models and demos can be found at: https://audio-agi.github.io/FlowSep_demo/.

While large language models (LLMs) are increasingly adapted for recommendation systems via supervised fine-tuning (SFT), this approach amplifies popularity bias due to its likelihood maximization objective, compromising recommendation diversity and fairness. To address this, we present Flow-guided fine-tuning recommender (Flower), which replaces SFT with a Generative Flow Network (GFlowNet) framework that enacts process supervision through token-level reward propagation. Flower's key innovation lies in decomposing item-level rewards into constituent token rewards, enabling direct alignment between token generation probabilities and their reward signals. This mechanism achieves three critical advancements: (1) popularity bias mitigation and fairness enhancement through empirical distribution matching, (2) preservation of diversity through GFlowNet's proportional sampling, and (3) flexible integration of personalized preferences via adaptable token rewards. Experiments demonstrate Flower's superior distribution-fitting capability and its significant advantages over traditional SFT in terms of fairness, diversity, and accuracy, highlighting its potential to improve LLM-based recommendation systems. The implementation is available via https://github.com/Mr-Peach0301/Flower

Transformers based on the attention mechanism have achieved impressive success in various areas. However, the attention mechanism has a quadratic complexity, significantly impeding Transformers from dealing with numerous tokens and scaling up to bigger models. Previous methods mainly utilize the similarity decomposition and the associativity of matrix multiplication to devise linear-time attention mechanisms. They avoid degeneration of attention to a trivial distribution by reintroducing inductive biases such as the locality, thereby at the expense of model generality and expressiveness. In this paper, we linearize Transformers free from specific inductive biases based on the flow network theory. We cast attention as the information flow aggregated from the sources (values) to the sinks (results) through the learned flow capacities (attentions). Within this framework, we apply the property of flow conservation into attention and propose the Flow-Attention mechanism of linear complexity. By respectively conserving the incoming flow of sinks for source competition and the outgoing flow of sources for sink allocation, Flow-Attention inherently generates informative attentions without using specific inductive biases. Empowered by the Flow-Attention, Flowformer yields strong performance in linear time for wide areas, including long sequence, time series, vision, natural language, and reinforcement learning. The code and settings are available at this repository: https://github.com/thuml/Flowformer.

Flow-based generative models have achieved remarkable progress, with classifier-free guidance (CFG) becoming the standard for high-fidelity generation. However, the conventional practice of applying a strong, fixed guidance scale throughout inference is poorly suited for the rapid, few-step sampling required by modern applications. In this work, we uncover the root cause of this conflict: a fundamental sampling instability where the earliest steps are acutely sensitive to guidance. We trace this to a significant spike in the ratio of conditional to unconditional predictions--a spike that we prove to be an inherent property of the training data distribution itself, making it a almost inevitable challenge. Applying a high, static guidance value during this volatile initial phase leads to an exponential amplification of error, degrading image quality. To resolve this, we propose a simple, theoretically grounded, adaptive guidance schedule that automatically dampens the guidance scale at early steps based on the evolving ratio. Our method is lightweight, incurs no inference overhead, and is compatible with standard frameworks. Experiments across state-of-the-art image (SD3.5, Qwen-Image) and video (WAN2.1) models show our approach enables up to 3x faster sampling while maintaining or improving quality, robustness, and semantic alignment. Our findings highlight that adapting guidance to the sampling process, rather than fixing it, is critical for unlocking the full potential of fast, flow-based models.

Extracting optical flow from videos remains a core computer vision problem. Motivated by the success of large general-purpose models, we ask whether frozen self-supervised video models trained only for future frame prediction can be prompted, without fine-tuning, to output flow. Prior work reading out depth or illumination from video generators required fine-tuning, which is impractical for flow where labels are scarce and synthetic datasets suffer from a sim-to-real gap. Inspired by the Counterfactual World Model (CWM) paradigm, which can obtain point-wise correspondences by injecting a small tracer perturbation into a next-frame predictor and tracking its propagation, we extend this idea to generative video models. We explore several popular architectures and find that successful zero-shot flow extraction in this manner is aided by three model properties: (1) distributional prediction of future frames (avoiding blurry or noisy outputs); (2) factorized latents that treat each spatio-temporal patch independently; and (3) random-access decoding that can condition on any subset of future pixels. These properties are uniquely present in the recent Local Random Access Sequence (LRAS) architecture. Building on LRAS, we propose KL-tracing: a novel test-time procedure that injects a localized perturbation into the first frame, rolls out the model one step, and computes the Kullback-Leibler divergence between perturbed and unperturbed predictive distributions. Without any flow-specific fine-tuning, our method outperforms state-of-the-art models on real-world TAP-Vid DAVIS dataset (16.6% relative improvement for endpoint error) and synthetic TAP-Vid Kubric (4.7% relative improvement). Our results indicate that counterfactual prompting of controllable generative video models is a scalable and effective alternative to supervised or photometric-loss approaches for high-quality flow.

Flow-based latent generative models such as Stable Diffusion 3 are able to generate images with remarkable quality, even enabling photorealistic text-to-image generation. Their impressive performance suggests that these models should also constitute powerful priors for inverse imaging problems, but that approach has not yet led to comparable fidelity. There are several key obstacles: (i) the encoding into a lower-dimensional latent space makes the underlying (forward) mapping non-linear; (ii) the data likelihood term is usually intractable; and (iii) learned generative models struggle to recover rare, atypical data modes during inference. We present FLAIR, a novel training free variational framework that leverages flow-based generative models as a prior for inverse problems. To that end, we introduce a variational objective for flow matching that is agnostic to the type of degradation, and combine it with deterministic trajectory adjustments to recover atypical modes. To enforce exact consistency with the observed data, we decouple the optimization of the data fidelity and regularization terms. Moreover, we introduce a time-dependent calibration scheme in which the strength of the regularization is modulated according to off-line accuracy estimates. Results on standard imaging benchmarks demonstrate that FLAIR consistently outperforms existing diffusion- and flow-based methods in terms of reconstruction quality and sample diversity.

Group Relative Policy Optimization (GRPO) has shown strong potential for flow-matching-based text-to-image (T2I) generation, but it faces two key limitations: inaccurate advantage attribution, and the neglect of temporal dynamics of generation. In this work, we argue that shifting the optimization paradigm from the step level to the chunk level can effectively alleviate these issues. Building on this idea, we propose Chunk-GRPO, the first chunk-level GRPO-based approach for T2I generation. The insight is to group consecutive steps into coherent 'chunk's that capture the intrinsic temporal dynamics of flow matching, and to optimize policies at the chunk level. In addition, we introduce an optional weighted sampling strategy to further enhance performance. Extensive experiments show that ChunkGRPO achieves superior results in both preference alignment and image quality, highlighting the promise of chunk-level optimization for GRPO-based methods.

We introduce a novel generative model for video prediction based on latent flow matching, an efficient alternative to diffusion-based models. In contrast to prior work, we keep the high costs of modeling the past during training and inference at bay by conditioning only on a small random set of past frames at each integration step of the image generation process. Moreover, to enable the generation of high-resolution videos and to speed up the training, we work in the latent space of a pretrained VQGAN. Finally, we propose to approximate the initial condition of the flow ODE with the previous noisy frame. This allows to reduce the number of integration steps and hence, speed up the sampling at inference time. We call our model Random frame conditioned flow Integration for VidEo pRediction, or, in short, RIVER. We show that RIVER achieves superior or on par performance compared to prior work on common video prediction benchmarks, while requiring an order of magnitude fewer computational resources.

We present FlowDet, the first formulation of object detection using modern Conditional Flow Matching techniques. This work follows from DiffusionDet, which originally framed detection as a generative denoising problem in the bounding box space via diffusion. We revisit and generalise this formulation to a broader class of generative transport problems, while maintaining the ability to vary the number of boxes and inference steps without re-training. In contrast to the curved stochastic transport paths induced by diffusion, FlowDet learns simpler and straighter paths resulting in faster scaling of detection performance as the number of inference steps grows. We find that this reformulation enables us to outperform diffusion based detection systems (as well as non-generative baselines) across a wide range of experiments, including various precision/recall operating points using multiple feature backbones and datasets. In particular, when evaluating under recall-constrained settings, we can highlight the effects of the generative transport without over-compensating with large numbers of proposals. This provides gains of up to +3.6% AP and +4.2% AP_{rare} over DiffusionDet on the COCO and LVIS datasets, respectively.

Visual tokenizers play a crucial role in diffusion models. The dimensionality of latent space governs both reconstruction fidelity and the semantic expressiveness of the latent feature. However, a fundamental trade-off is inherent between dimensionality and generation quality, constraining existing methods to low-dimensional latent spaces. Although recent works have leveraged vision foundation models to enrich the semantics of visual tokenizers and accelerate convergence, high-dimensional tokenizers still underperform their low-dimensional counterparts. In this work, we propose RecTok, which overcomes the limitations of high-dimensional visual tokenizers through two key innovations: flow semantic distillation and reconstruction--alignment distillation. Our key insight is to make the forward flow in flow matching semantically rich, which serves as the training space of diffusion transformers, rather than focusing on the latent space as in previous works. Specifically, our method distills the semantic information in VFMs into the forward flow trajectories in flow matching. And we further enhance the semantics by introducing a masked feature reconstruction loss. Our RecTok achieves superior image reconstruction, generation quality, and discriminative performance. It achieves state-of-the-art results on the gFID-50K under both with and without classifier-free guidance settings, while maintaining a semantically rich latent space structure. Furthermore, as the latent dimensionality increases, we observe consistent improvements. Code and model are available at https://shi-qingyu.github.io/rectok.github.io.

Denoising generative models, such as diffusion and flow-based models, produce high-quality samples but require many denoising steps due to discretization error. Flow maps, which estimate the average velocity between timesteps, mitigate this error and enable faster sampling. However, their training typically demands architectural changes that limit compatibility with pretrained flow models. We introduce Decoupled MeanFlow, a simple decoding strategy that converts flow models into flow map models without architectural modifications. Our method conditions the final blocks of diffusion transformers on the subsequent timestep, allowing pretrained flow models to be directly repurposed as flow maps. Combined with enhanced training techniques, this design enables high-quality generation in as few as 1 to 4 steps. Notably, we find that training flow models and subsequently converting them is more efficient and effective than training flow maps from scratch. On ImageNet 256x256 and 512x512, our models attain 1-step FID of 2.16 and 2.12, respectively, surpassing prior art by a large margin. Furthermore, we achieve FID of 1.51 and 1.68 when increasing the steps to 4, which nearly matches the performance of flow models while delivering over 100x faster inference.

Detector simulations are an exciting application of modern generative networks. Their sparse high-dimensional data combined with the required precision poses a serious challenge. We show how combining Conditional Flow Matching with transformer elements allows us to simulate the detector phase space reliably. Namely, we use an autoregressive transformer to simulate the energy of each layer, and a vision transformer for the high-dimensional voxel distributions. We show how dimension reduction via latent diffusion allows us to train more efficiently and how diffusion networks can be evaluated faster with bespoke solvers. We showcase our framework, CaloDREAM, on datasets 2 and 3 of the CaloChallenge.

Monocular depth estimation is crucial for numerous downstream vision tasks and applications. Current discriminative approaches to this problem are limited due to blurry artifacts, while state-of-the-art generative methods suffer from slow sampling due to their SDE nature. Rather than starting from noise, we seek a direct mapping from input image to depth map. We observe that this can be effectively framed using flow matching, since its straight trajectories through solution space offer efficiency and high quality. Our study demonstrates that a pre-trained image diffusion model can serve as an adequate prior for a flow matching depth model, allowing efficient training on only synthetic data to generalize to real images. We find that an auxiliary surface normals loss further improves the depth estimates. Due to the generative nature of our approach, our model reliably predicts the confidence of its depth estimates. On standard benchmarks of complex natural scenes, our lightweight approach exhibits state-of-the-art performance at favorable low computational cost despite only being trained on little synthetic data.

Flow matching has emerged as a compelling generative modeling approach that is widely used across domains. To generate data via a flow matching model, an ordinary differential equation (ODE) is numerically solved via forward integration of the modeled velocity field. To better capture the multi-modality that is inherent in typical velocity fields, hierarchical flow matching was recently introduced. It uses a hierarchy of ODEs that are numerically integrated when generating data. This hierarchy of ODEs captures the multi-modal velocity distribution just like vanilla flow matching is capable of modeling a multi-modal data distribution. While this hierarchy enables to model multi-modal velocity distributions, the complexity of the modeled distribution remains identical across levels of the hierarchy. In this paper, we study how to gradually adjust the complexity of the distributions across different levels of the hierarchy via mini-batch couplings. We show the benefits of mini-batch couplings in hierarchical rectified flow matching via compelling results on synthetic and imaging data. Code is available at https://riccizz.github.io/HRF_coupling.

We propose a principled and effective framework for one-step generative modeling. We introduce the notion of average velocity to characterize flow fields, in contrast to instantaneous velocity modeled by Flow Matching methods. A well-defined identity between average and instantaneous velocities is derived and used to guide neural network training. Our method, termed the MeanFlow model, is self-contained and requires no pre-training, distillation, or curriculum learning. MeanFlow demonstrates strong empirical performance: it achieves an FID of 3.43 with a single function evaluation (1-NFE) on ImageNet 256x256 trained from scratch, significantly outperforming previous state-of-the-art one-step diffusion/flow models. Our study substantially narrows the gap between one-step diffusion/flow models and their multi-step predecessors, and we hope it will motivate future research to revisit the foundations of these powerful models.

Existing graph matching methods typically assume that there are similar structures between graphs and they are matchable. However, these assumptions do not align with real-world applications. This work addresses a more realistic scenario where graphs exhibit diverse modes, requiring graph grouping before or along with matching, a task termed mixture graph matching and clustering. We introduce Minorize-Maximization Matching and Clustering (M3C), a learning-free algorithm that guarantees theoretical convergence through the Minorize-Maximization framework and offers enhanced flexibility via relaxed clustering. Building on M3C, we develop UM3C, an unsupervised model that incorporates novel edge-wise affinity learning and pseudo label selection. Extensive experimental results on public benchmarks demonstrate that our method outperforms state-of-the-art graph matching and mixture graph matching and clustering approaches in both accuracy and efficiency. Source code will be made publicly available.

Recent flow matching models for text-to-image generation have achieved remarkable quality, yet their integration with reinforcement learning for human preference alignment remains suboptimal, hindering fine-grained reward-based optimization. We observe that the key impediment to effective GRPO training of flow models is the temporal uniformity assumption in existing approaches: sparse terminal rewards with uniform credit assignment fail to capture the varying criticality of decisions across generation timesteps, resulting in inefficient exploration and suboptimal convergence. To remedy this shortcoming, we introduce TempFlow-GRPO (Temporal Flow GRPO), a principled GRPO framework that captures and exploits the temporal structure inherent in flow-based generation. TempFlow-GRPO introduces two key innovations: (i) a trajectory branching mechanism that provides process rewards by concentrating stochasticity at designated branching points, enabling precise credit assignment without requiring specialized intermediate reward models; and (ii) a noise-aware weighting scheme that modulates policy optimization according to the intrinsic exploration potential of each timestep, prioritizing learning during high-impact early stages while ensuring stable refinement in later phases. These innovations endow the model with temporally-aware optimization that respects the underlying generative dynamics, leading to state-of-the-art performance in human preference alignment and standard text-to-image benchmarks.

Vision-Language-Action (VLA) models trained with flow matching have demonstrated impressive capabilities on robotic manipulation tasks. However, their performance often degrades under distribution shift and on complex multi-step tasks, suggesting that the learned representations may not robustly capture task-relevant semantics. We introduce DiG-Flow, a principled framework that enhances VLA robustness through geometric regularization. Our key insight is that the distributional discrepancy between observation and action embeddings provides a meaningful geometric signal: lower transport cost indicates compatible representations, while higher cost suggests potential misalignment. DiG-Flow computes a discrepancy measure between empirical distributions of observation and action embeddings, maps it to a modulation weight via a monotone function, and applies residual updates to the observation embeddings before flow matching. Crucially, this intervention operates at the representation level without modifying the flow matching path or target vector field. We provide theoretical guarantees showing that discrepancy-guided training provably decreases the training objective, and that guided inference refinement converges with contraction. Empirically, DiG-Flow integrates into existing VLA architectures with negligible overhead and consistently improves performance, with particularly pronounced gains on complex multi-step tasks and under limited training data.

Video inpainting, which aims at filling in missing regions of a video, remains challenging due to the difficulty of preserving the precise spatial and temporal coherence of video contents. In this work we propose a novel flow-guided video inpainting approach. Rather than filling in the RGB pixels of each frame directly, we consider video inpainting as a pixel propagation problem. We first synthesize a spatially and temporally coherent optical flow field across video frames using a newly designed Deep Flow Completion network. Then the synthesized flow field is used to guide the propagation of pixels to fill up the missing regions in the video. Specifically, the Deep Flow Completion network follows a coarse-to-fine refinement to complete the flow fields, while their quality is further improved by hard flow example mining. Following the guide of the completed flow, the missing video regions can be filled up precisely. Our method is evaluated on DAVIS and YouTube-VOS datasets qualitatively and quantitatively, achieving the state-of-the-art performance in terms of inpainting quality and speed.

We present M^3-Bench, the first benchmark for evaluating multimodal tool use under the Model Context Protocol. The benchmark targets realistic, multi-hop and multi-threaded workflows that require visual grounding and textual reasoning, cross-tool dependencies, and persistence of intermediate resources across steps. We introduce a similarity-driven alignment that serializes each tool call, embeds signatures with a sentence encoder, and performs similarity-bucketed Hungarian matching to obtain auditable one-to-one correspondences. On top of this alignment, we report interpretable metrics that decouple semantic fidelity from workflow consistency. The benchmark spans 28 servers with 231 tools, and provides standardized trajectories curated through an Executor & Judge pipeline with human verification; an auxiliary four large language models (LLMs) judge ensemble reports end-task Task Completion and information grounding. Evaluations of representative state-of-the-art Multimodal LLMs (MLLMs) reveal persistent gaps in multimodal MCP tool use, particularly in argument fidelity and structure consistency, underscoring the need for methods that jointly reason over images, text, and tool graphs. Our Benchmark's anonymous repository is at https://github.com/EtaYang10th/Open-M3-Bench

Transformers, the standard implementation for large language models (LLMs), typically consist of tens to hundreds of discrete layers. While more layers can lead to better performance, this approach has been challenged as far from efficient, especially given the superiority of continuous layers demonstrated by diffusion and flow-based models for image generation. We propose the Latent Flow Transformer (LFT), which replaces a block of layers with a single learned transport operator trained via flow matching, offering significant compression while maintaining compatibility with the original architecture. Additionally, we address the limitations of existing flow-based methods in preserving coupling by introducing the Flow Walking (FW) algorithm. On the Pythia-410M model, LFT trained with flow matching compresses 6 of 24 layers and outperforms directly skipping 2 layers (KL Divergence of LM logits at 0.407 vs. 0.529), demonstrating the feasibility of this design. When trained with FW, LFT further distills 12 layers into one while reducing the KL to 0.736 surpassing that from skipping 3 layers (0.932), significantly narrowing the gap between autoregressive and flow-based generation paradigms.

Continuous normalizing flows (CNFs) are an attractive generative modeling technique, but they have been held back by limitations in their simulation-based maximum likelihood training. We introduce the generalized conditional flow matching (CFM) technique, a family of simulation-free training objectives for CNFs. CFM features a stable regression objective like that used to train the stochastic flow in diffusion models but enjoys the efficient inference of deterministic flow models. In contrast to both diffusion models and prior CNF training algorithms, CFM does not require the source distribution to be Gaussian or require evaluation of its density. A variant of our objective is optimal transport CFM (OT-CFM), which creates simpler flows that are more stable to train and lead to faster inference, as evaluated in our experiments. Furthermore, we show that when the true OT plan is available, our OT-CFM method approximates dynamic OT. Training CNFs with CFM improves results on a variety of conditional and unconditional generation tasks, such as inferring single cell dynamics, unsupervised image translation, and Schr\"odinger bridge inference.

We introduce RapFlow-TTS, a rapid and high-fidelity TTS acoustic model that leverages velocity consistency constraints in flow matching (FM) training. Although ordinary differential equation (ODE)-based TTS generation achieves natural-quality speech, it typically requires a large number of generation steps, resulting in a trade-off between quality and inference speed. To address this challenge, RapFlow-TTS enforces consistency in the velocity field along the FM-straightened ODE trajectory, enabling consistent synthetic quality with fewer generation steps. Additionally, we introduce techniques such as time interval scheduling and adversarial learning to further enhance the quality of the few-step synthesis. Experimental results show that RapFlow-TTS achieves high-fidelity speech synthesis with a 5- and 10-fold reduction in synthesis steps than the conventional FM- and score-based approaches, respectively.

Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for learning stochastic process priors on function spaces. OFM provides the probability density of the values of any collection of points and enables mathematically tractable functional regression at new points with mean and density estimation. Our method outperforms state-of-the-art models in stochastic process learning, functional regression, and prior learning.

In this paper, we establish a connection between the parameterization of flow-based and energy-based generative models, and present a new flow-based modeling approach called energy-based normalizing flow (EBFlow). We demonstrate that by optimizing EBFlow with score-matching objectives, the computation of Jacobian determinants for linear transformations can be entirely bypassed. This feature enables the use of arbitrary linear layers in the construction of flow-based models without increasing the computational time complexity of each training iteration from O(D^2L) to O(D^3L) for an L-layered model that accepts D-dimensional inputs. This makes the training of EBFlow more efficient than the commonly-adopted maximum likelihood training method. In addition to the reduction in runtime, we enhance the training stability and empirical performance of EBFlow through a number of techniques developed based on our analysis of the score-matching methods. The experimental results demonstrate that our approach achieves a significant speedup compared to maximum likelihood estimation while outperforming prior methods with a noticeable margin in terms of negative log-likelihood (NLL).

Generative machine learning methods, such as diffusion models and flow matching, have shown great potential in modeling complex system behaviors and building efficient surrogate models. However, these methods typically learn the underlying physics implicitly from data. We propose Physics-Based Flow Matching (PBFM), a novel generative framework that explicitly embeds physical constraints, both PDE residuals and algebraic relations, into the flow matching objective. We also introduce temporal unrolling at training time that improves the accuracy of the final, noise-free sample prediction. Our method jointly minimizes the flow matching loss and the physics-based residual loss without requiring hyperparameter tuning of their relative weights. Additionally, we analyze the role of the minimum noise level, sigma_{min}, in the context of physical constraints and evaluate a stochastic sampling strategy that helps to reduce physical residuals. Through extensive benchmarks on three representative PDE problems, we show that our approach yields up to an 8times more accurate physical residuals compared to FM, while clearly outperforming existing algorithms in terms of distributional accuracy. PBFM thus provides a principled and efficient framework for surrogate modeling, uncertainty quantification, and accelerated simulation in physics and engineering applications.

A "match cut" is a common video editing technique where a pair of shots that have a similar composition transition fluidly from one to another. Although match cuts are often visual, certain match cuts involve the fluid transition of audio, where sounds from different sources merge into one indistinguishable transition between two shots. In this paper, we explore the ability to automatically find and create "audio match cuts" within videos and movies. We create a self-supervised audio representation for audio match cutting and develop a coarse-to-fine audio match pipeline that recommends matching shots and creates the blended audio. We further annotate a dataset for the proposed audio match cut task and compare the ability of multiple audio representations to find audio match cut candidates. Finally, we evaluate multiple methods to blend two matching audio candidates with the goal of creating a smooth transition. Project page and examples are available at: https://denfed.github.io/audiomatchcut/

Information flows by routes inside the network via mechanisms implemented in the model. These routes can be represented as graphs where nodes correspond to token representations and edges to operations inside the network. We automatically build these graphs in a top-down manner, for each prediction leaving only the most important nodes and edges. In contrast to the existing workflows relying on activation patching, we do this through attribution: this allows us to efficiently uncover existing circuits with just a single forward pass. Additionally, the applicability of our method is far beyond patching: we do not need a human to carefully design prediction templates, and we can extract information flow routes for any prediction (not just the ones among the allowed templates). As a result, we can talk about model behavior in general, for specific types of predictions, or different domains. We experiment with Llama 2 and show that the role of some attention heads is overall important, e.g. previous token heads and subword merging heads. Next, we find similarities in Llama 2 behavior when handling tokens of the same part of speech. Finally, we show that some model components can be specialized on domains such as coding or multilingual texts.

Large Language Models (LLMs) perform well on familiar queries but struggle with specialized or emerging topics. Graph-based Retrieval-Augmented Generation (GraphRAG) addresses this by structuring domain knowledge as a graph for dynamic retrieval. However, existing pipelines involve complex engineering workflows, making it difficult to isolate the impact of individual components. Evaluating retrieval effectiveness is also challenging due to dataset overlap with LLM pretraining data. In this work, we introduce HuixiangDou2, a robustly optimized GraphRAG framework. Specifically, we leverage the effectiveness of dual-level retrieval and optimize its performance in a 32k context for maximum precision, and compare logic-based retrieval and dual-level retrieval to enhance overall functionality. Our implementation includes comparative experiments on a test set, where Qwen2.5-7B-Instruct initially underperformed. With our approach, the score improved significantly from 60 to 74.5, as illustrated in the Figure. Experiments on domain-specific datasets reveal that dual-level retrieval enhances fuzzy matching, while logic-form retrieval improves structured reasoning. Furthermore, we propose a multi-stage verification mechanism to improve retrieval robustness without increasing computational cost. Empirical results show significant accuracy gains over baselines, highlighting the importance of adaptive retrieval. To support research and adoption, we release HuixiangDou2 as an open-source resource https://github.com/tpoisonooo/huixiangdou2.

Diffusion models have revolutionized the field of content synthesis and editing. Recent models have replaced the traditional UNet architecture with the Diffusion Transformer (DiT), and employed flow-matching for improved training and sampling. However, they exhibit limited generation diversity. In this work, we leverage this limitation to perform consistent image edits via selective injection of attention features. The main challenge is that, unlike the UNet-based models, DiT lacks a coarse-to-fine synthesis structure, making it unclear in which layers to perform the injection. Therefore, we propose an automatic method to identify "vital layers" within DiT, crucial for image formation, and demonstrate how these layers facilitate a range of controlled stable edits, from non-rigid modifications to object addition, using the same mechanism. Next, to enable real-image editing, we introduce an improved image inversion method for flow models. Finally, we evaluate our approach through qualitative and quantitative comparisons, along with a user study, and demonstrate its effectiveness across multiple applications. The project page is available at https://omriavrahami.com/stable-flow

Large Language Models (LLMs) are primarily designed for batch processing. Existing methods for adapting LLMs to streaming rely either on expensive re-encoding or specialized architectures with limited scalability. This work identifies three key mismatches in adapting batch-oriented LLMs to streaming: (1) input-attention, (2) output-attention, and (3) position-ID mismatches. While it is commonly assumed that the latter two mismatches require frequent re-encoding, our analysis reveals that only the input-attention mismatch significantly impacts performance, indicating re-encoding outputs is largely unnecessary. To better understand this discrepancy with the common assumption, we provide the first comprehensive analysis of the impact of position encoding on LLMs in streaming, showing that preserving relative positions within source and target contexts is more critical than maintaining absolute order. Motivated by the above analysis, we introduce a group position encoding paradigm built on batch architectures to enhance consistency between streaming and batch modes. Extensive experiments on cross-lingual and cross-modal tasks demonstrate that our method outperforms existing approaches. Our method requires no architectural modifications, exhibits strong generalization in both streaming and batch modes. The code is available at repository https://github.com/EIT-NLP/StreamingLLM.

Text-driven video editing aims to modify video content according to natural language instructions. While recent training-free approaches have made progress by leveraging pre-trained diffusion models, they typically rely on inversion-based techniques that map input videos into the latent space, which often leads to temporal inconsistencies and degraded structural fidelity. To address this, we propose FlowDirector, a novel inversion-free video editing framework. Our framework models the editing process as a direct evolution in data space, guiding the video via an Ordinary Differential Equation (ODE) to smoothly transition along its inherent spatiotemporal manifold, thereby preserving temporal coherence and structural details. To achieve localized and controllable edits, we introduce an attention-guided masking mechanism that modulates the ODE velocity field, preserving non-target regions both spatially and temporally. Furthermore, to address incomplete edits and enhance semantic alignment with editing instructions, we present a guidance-enhanced editing strategy inspired by Classifier-Free Guidance, which leverages differential signals between multiple candidate flows to steer the editing trajectory toward stronger semantic alignment without compromising structural consistency. Extensive experiments across benchmarks demonstrate that FlowDirector achieves state-of-the-art performance in instruction adherence, temporal consistency, and background preservation, establishing a new paradigm for efficient and coherent video editing without inversion.

Flowcharts are graphical tools for representing complex concepts in concise visual representations. This paper introduces the FlowLearn dataset, a resource tailored to enhance the understanding of flowcharts. FlowLearn contains complex scientific flowcharts and simulated flowcharts. The scientific subset contains 3,858 flowcharts sourced from scientific literature and the simulated subset contains 10,000 flowcharts created using a customizable script. The dataset is enriched with annotations for visual components, OCR, Mermaid code representation, and VQA question-answer pairs. Despite the proven capabilities of Large Vision-Language Models (LVLMs) in various visual understanding tasks, their effectiveness in decoding flowcharts - a crucial element of scientific communication - has yet to be thoroughly investigated. The FlowLearn test set is crafted to assess the performance of LVLMs in flowchart comprehension. Our study thoroughly evaluates state-of-the-art LVLMs, identifying existing limitations and establishing a foundation for future enhancements in this relatively underexplored domain. For instance, in tasks involving simulated flowcharts, GPT-4V achieved the highest accuracy (58%) in counting the number of nodes, while Claude recorded the highest accuracy (83%) in OCR tasks. Notably, no single model excels in all tasks within the FlowLearn framework, highlighting significant opportunities for further development.

Flow-based generative models (Dinh et al., 2014) are conceptually attractive due to tractability of the exact log-likelihood, tractability of exact latent-variable inference, and parallelizability of both training and synthesis. In this paper we propose Glow, a simple type of generative flow using an invertible 1x1 convolution. Using our method we demonstrate a significant improvement in log-likelihood on standard benchmarks. Perhaps most strikingly, we demonstrate that a generative model optimized towards the plain log-likelihood objective is capable of efficient realistic-looking synthesis and manipulation of large images. The code for our model is available at https://github.com/openai/glow

Diffusion and flow-based non-autoregressive (NAR) models have shown strong promise in large language modeling, however, their potential for automatic speech recognition (ASR) remains largely unexplored. We propose Drax, a discrete flow matching framework for ASR that enables efficient parallel decoding. To better align training with inference, we construct an audio-conditioned probability path that guides the model through trajectories resembling likely intermediate inference errors, rather than direct random noise to target transitions. Our theoretical analysis links the generalization gap to divergences between training and inference occupancies, controlled by cumulative velocity errors, thereby motivating our design choice. Empirical evaluation demonstrates that our approach attains recognition accuracy on par with state-of-the-art speech models while offering improved accuracy-efficiency trade-offs, highlighting discrete flow matching as a promising direction for advancing NAR ASR.

We propose Flow-GRPO, the first method integrating online reinforcement learning (RL) into flow matching models. Our approach uses two key strategies: (1) an ODE-to-SDE conversion that transforms a deterministic Ordinary Differential Equation (ODE) into an equivalent Stochastic Differential Equation (SDE) that matches the original model's marginal distribution at all timesteps, enabling statistical sampling for RL exploration; and (2) a Denoising Reduction strategy that reduces training denoising steps while retaining the original inference timestep number, significantly improving sampling efficiency without performance degradation. Empirically, Flow-GRPO is effective across multiple text-to-image tasks. For complex compositions, RL-tuned SD3.5 generates nearly perfect object counts, spatial relations, and fine-grained attributes, boosting GenEval accuracy from 63% to 95%. In visual text rendering, its accuracy improves from 59% to 92%, significantly enhancing text generation. Flow-GRPO also achieves substantial gains in human preference alignment. Notably, little to no reward hacking occurred, meaning rewards did not increase at the cost of image quality or diversity, and both remained stable in our experiments.

Current scene flow methods broadly fail to describe motion on small objects, and current scene flow evaluation protocols hide this failure by averaging over many points, with most drawn larger objects. To fix this evaluation failure, we propose a new evaluation protocol, Bucket Normalized EPE, which is class-aware and speed-normalized, enabling contextualized error comparisons between object types that move at vastly different speeds. To highlight current method failures, we propose a frustratingly simple supervised scene flow baseline, TrackFlow, built by bolting a high-quality pretrained detector (trained using many class rebalancing techniques) onto a simple tracker, that produces state-of-the-art performance on current standard evaluations and large improvements over prior art on our new evaluation. Our results make it clear that all scene flow evaluations must be class and speed aware, and supervised scene flow methods must address point class imbalances. We release the evaluation code publicly at https://github.com/kylevedder/BucketedSceneFlowEval.

We present evaluation results for FLUX.1 Kontext, a generative flow matching model that unifies image generation and editing. The model generates novel output views by incorporating semantic context from text and image inputs. Using a simple sequence concatenation approach, FLUX.1 Kontext handles both local editing and generative in-context tasks within a single unified architecture. Compared to current editing models that exhibit degradation in character consistency and stability across multiple turns, we observe that FLUX.1 Kontext improved preservation of objects and characters, leading to greater robustness in iterative workflows. The model achieves competitive performance with current state-of-the-art systems while delivering significantly faster generation times, enabling interactive applications and rapid prototyping workflows. To validate these improvements, we introduce KontextBench, a comprehensive benchmark with 1026 image-prompt pairs covering five task categories: local editing, global editing, character reference, style reference and text editing. Detailed evaluations show the superior performance of FLUX.1 Kontext in terms of both single-turn quality and multi-turn consistency, setting new standards for unified image processing models.

Normalizing flows (NFs) have become a prominent method for deep generative models that allow for an analytic probability density estimation and efficient synthesis. However, a flow-based network is considered to be inefficient in parameter complexity because of reduced expressiveness of bijective mapping, which renders the models unfeasibly expensive in terms of parameters. We present an alternative parameterization scheme called NanoFlow, which uses a single neural density estimator to model multiple transformation stages. Hence, we propose an efficient parameter decomposition method and the concept of flow indication embedding, which are key missing components that enable density estimation from a single neural network. Experiments performed on audio and image models confirm that our method provides a new parameter-efficient solution for scalable NFs with significant sublinear parameter complexity.

To advance continuous-valued token modeling and temporal-coherence enforcement, we propose FELLE, an autoregressive model that integrates language modeling with token-wise flow matching. By leveraging the autoregressive nature of language models and the generative efficacy of flow matching, FELLE effectively predicts continuous-valued tokens (mel-spectrograms). For each continuous-valued token, FELLE modifies the general prior distribution in flow matching by incorporating information from the previous step, improving coherence and stability. Furthermore, to enhance synthesis quality, FELLE introduces a coarse-to-fine flow-matching mechanism, generating continuous-valued tokens hierarchically, conditioned on the language model's output. Experimental results demonstrate the potential of incorporating flow-matching techniques in autoregressive mel-spectrogram modeling, leading to significant improvements in TTS generation quality, as shown in https://aka.ms/felle.

Recently, text-to-speech (TTS) models such as FastSpeech and ParaNet have been proposed to generate mel-spectrograms from text in parallel. Despite the advantage, the parallel TTS models cannot be trained without guidance from autoregressive TTS models as their external aligners. In this work, we propose Glow-TTS, a flow-based generative model for parallel TTS that does not require any external aligner. By combining the properties of flows and dynamic programming, the proposed model searches for the most probable monotonic alignment between text and the latent representation of speech on its own. We demonstrate that enforcing hard monotonic alignments enables robust TTS, which generalizes to long utterances, and employing generative flows enables fast, diverse, and controllable speech synthesis. Glow-TTS obtains an order-of-magnitude speed-up over the autoregressive model, Tacotron 2, at synthesis with comparable speech quality. We further show that our model can be easily extended to a multi-speaker setting.

Normalizing Flows (NFs) are a class of generative models distinguished by a mathematically invertible architecture, where the forward pass transforms data into a latent space for density estimation, and the reverse pass generates new samples from this space. This characteristic creates an intrinsic synergy between representation learning and data generation. However, the generative quality of standard NFs is limited by poor semantic representations from log-likelihood optimization. To remedy this, we propose a novel alignment strategy that creatively leverages the invertibility of NFs: instead of regularizing the forward pass, we align the intermediate features of the generative (reverse) pass with representations from a powerful vision foundation model, demonstrating superior effectiveness over naive alignment. We also introduce a novel training-free, test-time optimization algorithm for classification, which provides a more intrinsic evaluation of the NF's embedded semantic knowledge. Comprehensive experiments demonstrate that our approach accelerates the training of NFs by over 3.3times, while simultaneously delivering significant improvements in both generative quality and classification accuracy. New state-of-the-art results for NFs are established on ImageNet 64times64 and 256times256. Our code is available at https://github.com/MCG-NJU/FlowBack.

In this work, we introduce Modulated Flows (ModFlows), a novel approach for color transfer between images based on rectified flows. The primary goal of the color transfer is to adjust the colors of a target image to match the color distribution of a reference image. Our technique is based on optimal transport and executes color transfer as an invertible transformation within the RGB color space. The ModFlows utilizes the bijective property of flows, enabling us to introduce a common intermediate color distribution and build a dataset of rectified flows. We train an encoder on this dataset to predict the weights of a rectified model for new images. After training on a set of optimal transport plans, our approach can generate plans for new pairs of distributions without additional fine-tuning. We additionally show that the trained encoder provides an image embedding, associated only with its color style. The presented method is capable of processing 4K images and achieves the state-of-the-art performance in terms of content and style similarity. Our source code is available at https://github.com/maria-larchenko/modflows

With the rapid increase in the amount of public code repositories, developers maintain a great desire to retrieve precise code snippets by using natural language. Despite existing deep learning based approaches(e.g., DeepCS and MMAN) have provided the end-to-end solutions (i.e., accepts natural language as queries and shows related code fragments retrieved directly from code corpus), the accuracy of code search in the large-scale repositories is still limited by the code representation (e.g., AST) and modeling (e.g., directly fusing the features in the attention stage). In this paper, we propose a novel learnable deep Graph for Code Search (calleddeGraphCS), to transfer source code into variable-based flow graphs based on the intermediate representation technique, which can model code semantics more precisely compared to process the code as text directly or use the syntactic tree representation. Furthermore, we propose a well-designed graph optimization mechanism to refine the code representation, and apply an improved gated graph neural network to model variable-based flow graphs. To evaluate the effectiveness of deGraphCS, we collect a large-scale dataset from GitHub containing 41,152 code snippets written in C language, and reproduce several typical deep code search methods for comparison. Besides, we design a qualitative user study to verify the practical value of our approach. The experimental results have shown that deGraphCS can achieve state-of-the-art performances, and accurately retrieve code snippets satisfying the needs of the users.

We present a new scientific document similarity model based on matching fine-grained aspects of texts. To train our model, we exploit a naturally-occurring source of supervision: sentences in the full-text of papers that cite multiple papers together (co-citations). Such co-citations not only reflect close paper relatedness, but also provide textual descriptions of how the co-cited papers are related. This novel form of textual supervision is used for learning to match aspects across papers. We develop multi-vector representations where vectors correspond to sentence-level aspects of documents, and present two methods for aspect matching: (1) A fast method that only matches single aspects, and (2) a method that makes sparse multiple matches with an Optimal Transport mechanism that computes an Earth Mover's Distance between aspects. Our approach improves performance on document similarity tasks in four datasets. Further, our fast single-match method achieves competitive results, paving the way for applying fine-grained similarity to large scientific corpora. Code, data, and models available at: https://github.com/allenai/aspire

Leveraging visual priors from pre-trained text-to-image (T2I) generative models has shown success in dense prediction. However, dense prediction is inherently an image-to-image task, suggesting that image editing models, rather than T2I generative models, may be a more suitable foundation for fine-tuning. Motivated by this, we conduct a systematic analysis of the fine-tuning behaviors of both editors and generators for dense geometry estimation. Our findings show that editing models possess inherent structural priors, which enable them to converge more stably by ``refining" their innate features, and ultimately achieve higher performance than their generative counterparts. Based on these findings, we introduce FE2E, a framework that pioneeringly adapts an advanced editing model based on Diffusion Transformer (DiT) architecture for dense geometry prediction. Specifically, to tailor the editor for this deterministic task, we reformulate the editor's original flow matching loss into the ``consistent velocity" training objective. And we use logarithmic quantization to resolve the precision conflict between the editor's native BFloat16 format and the high precision demand of our tasks. Additionally, we leverage the DiT's global attention for a cost-free joint estimation of depth and normals in a single forward pass, enabling their supervisory signals to mutually enhance each other. Without scaling up the training data, FE2E achieves impressive performance improvements in zero-shot monocular depth and normal estimation across multiple datasets. Notably, it achieves over 35\% performance gains on the ETH3D dataset and outperforms the DepthAnything series, which is trained on 100times data. The project page can be accessed https://amap-ml.github.io/FE2E/{here}.

Diffusion and flow matching models have significantly advanced media generation, yet their design space is well-explored, somewhat limiting further improvements. Concurrently, autoregressive (AR) models, particularly those generating continuous tokens, have emerged as a promising direction for unifying text and media generation. This paper introduces Transition Matching (TM), a novel discrete-time, continuous-state generative paradigm that unifies and advances both diffusion/flow models and continuous AR generation. TM decomposes complex generation tasks into simpler Markov transitions, allowing for expressive non-deterministic probability transition kernels and arbitrary non-continuous supervision processes, thereby unlocking new flexible design avenues. We explore these choices through three TM variants: (i) Difference Transition Matching (DTM), which generalizes flow matching to discrete-time by directly learning transition probabilities, yielding state-of-the-art image quality and text adherence as well as improved sampling efficiency. (ii) Autoregressive Transition Matching (ARTM) and (iii) Full History Transition Matching (FHTM) are partially and fully causal models, respectively, that generalize continuous AR methods. They achieve continuous causal AR generation quality comparable to non-causal approaches and potentially enable seamless integration with existing AR text generation techniques. Notably, FHTM is the first fully causal model to match or surpass the performance of flow-based methods on text-to-image task in continuous domains. We demonstrate these contributions through a rigorous large-scale comparison of TM variants and relevant baselines, maintaining a fixed architecture, training data, and hyperparameters.

Dense image correspondence is central to many applications, such as visual odometry, 3D reconstruction, object association, and re-identification. Historically, dense correspondence has been tackled separately for wide-baseline scenarios and optical flow estimation, despite the common goal of matching content between two images. In this paper, we develop a Unified Flow & Matching model (UFM), which is trained on unified data for pixels that are co-visible in both source and target images. UFM uses a simple, generic transformer architecture that directly regresses the (u,v) flow. It is easier to train and more accurate for large flows compared to the typical coarse-to-fine cost volumes in prior work. UFM is 28% more accurate than state-of-the-art flow methods (Unimatch), while also having 62% less error and 6.7x faster than dense wide-baseline matchers (RoMa). UFM is the first to demonstrate that unified training can outperform specialized approaches across both domains. This result enables fast, general-purpose correspondence and opens new directions for multi-modal, long-range, and real-time correspondence tasks.

Flow-based 3D generation models typically require dozens of sampling steps during inference. Though few-step distillation methods, particularly Consistency Models (CMs), have achieved substantial advancements in accelerating 2D diffusion models, they remain under-explored for more complex 3D generation tasks. In this study, we propose a novel framework, MDT-dist, for few-step 3D flow distillation. Our approach is built upon a primary objective: distilling the pretrained model to learn the Marginal-Data Transport. Directly learning this objective needs to integrate the velocity fields, while this integral is intractable to be implemented. Therefore, we propose two optimizable objectives, Velocity Matching (VM) and Velocity Distillation (VD), to equivalently convert the optimization target from the transport level to the velocity and the distribution level respectively. Velocity Matching (VM) learns to stably match the velocity fields between the student and the teacher, but inevitably provides biased gradient estimates. Velocity Distillation (VD) further enhances the optimization process by leveraging the learned velocity fields to perform probability density distillation. When evaluated on the pioneer 3D generation framework TRELLIS, our method reduces sampling steps of each flow transformer from 25 to 1 or 2, achieving 0.68s (1 step x 2) and 0.94s (2 steps x 2) latency with 9.0x and 6.5x speedup on A800, while preserving high visual and geometric fidelity. Extensive experiments demonstrate that our method significantly outperforms existing CM distillation methods, and enables TRELLIS to achieve superior performance in few-step 3D generation.

Generative flow networks (GFlowNets) are a family of algorithms that learn a generative policy to sample discrete objects x with non-negative reward R(x). Learning objectives guarantee the GFlowNet samples x from the target distribution p^*(x) propto R(x) when loss is globally minimized over all states or trajectories, but it is unclear how well they perform with practical limits on training resources. We introduce an efficient evaluation strategy to compare the learned sampling distribution to the target reward distribution. As flows can be underdetermined given training data, we clarify the importance of learned flows to generalization and matching p^*(x) in practice. We investigate how to learn better flows, and propose (i) prioritized replay training of high-reward x, (ii) relative edge flow policy parametrization, and (iii) a novel guided trajectory balance objective, and show how it can solve a substructure credit assignment problem. We substantially improve sample efficiency on biochemical design tasks.

Optical flow estimation is a classical yet challenging task in computer vision. One of the essential factors in accurately predicting optical flow is to alleviate occlusions between frames. However, it is still a thorny problem for current top-performing optical flow estimation methods due to insufficient local evidence to model occluded areas. In this paper, we propose the Super Kernel Flow Network (SKFlow), a CNN architecture to ameliorate the impacts of occlusions on optical flow estimation. SKFlow benefits from the super kernels which bring enlarged receptive fields to complement the absent matching information and recover the occluded motions. We present efficient super kernel designs by utilizing conical connections and hybrid depth-wise convolutions. Extensive experiments demonstrate the effectiveness of SKFlow on multiple benchmarks, especially in the occluded areas. Without pre-trained backbones on ImageNet and with a modest increase in computation, SKFlow achieves compelling performance and ranks 1st among currently published methods on the Sintel benchmark. On the challenging Sintel clean and final passes (test), SKFlow surpasses the best-published result in the unmatched areas (7.96 and 12.50) by 9.09% and 7.92%. The code is available at https://github.com/littlespray/SKFlow{https://github.com/littlespray/SKFlow}.

We present FrameFlow, a method for fast protein backbone generation using SE(3) flow matching. Specifically, we adapt FrameDiff, a state-of-the-art diffusion model, to the flow-matching generative modeling paradigm. We show how flow matching can be applied on SE(3) and propose modifications during training to effectively learn the vector field. Compared to FrameDiff, FrameFlow requires five times fewer sampling timesteps while achieving two fold better designability. The ability to generate high quality protein samples at a fraction of the cost of previous methods paves the way towards more efficient generative models in de novo protein design.

Generative models have gained more and more attention in recent years for their remarkable success in tasks that required estimating and sampling data distribution to generate high-fidelity synthetic data. In speech, text-to-speech synthesis and neural vocoder are good examples where generative models have shined. While generative models have been applied to different applications in speech, there exists no general-purpose generative model that models speech directly. In this work, we take a step toward this direction by showing a single pre-trained generative model can be adapted to different downstream tasks with strong performance. Specifically, we pre-trained a generative model, named SpeechFlow, on 60k hours of untranscribed speech with Flow Matching and masked conditions. Experiment results show the pre-trained generative model can be fine-tuned with task-specific data to match or surpass existing expert models on speech enhancement, separation, and synthesis. Our work suggested a foundational model for generation tasks in speech can be built with generative pre-training.