11institutetext:  Sapienza University of Rome

# MoDiPO: text-to-motion alignment via AI-feedback-driven Direct Preference
Optimization

Massimiliano Pappa  Luca Collorone  Giovanni Ficarra  Indro Spinelli  Fabio
Galasso

###### Abstract

Diffusion Models have revolutionized the field of human motion generation by
offering exceptional generation quality and fine-grained controllability
through natural language conditioning. Their inherent stochasticity, that is
the ability to generate various outputs from a single input, is key to their
success. However, this diversity should not be unrestricted, as it may lead to
unlikely generations. Instead, it should be confined within the boundaries of
text-aligned and realistic generations. To address this issue, we propose
MoDiPO (Motion Diffusion DPO), a novel methodology that leverages Direct
Preference Optimization (DPO) to align text-to-motion models. We streamline
the laborious and expensive process of gathering human preferences needed in
DPO by leveraging AI feedback instead. This enables us to experiment with
novel DPO strategies, using both online and offline generated motion-
preference pairs. To foster future research we contribute with a motion-
preference dataset which we dub Pick-a-Move. We demonstrate, both
qualitatively and quantitatively, that our proposed method yields
significantly more realistic motions. In particular, MoDiPO substantially
improves Frechet Inception Distance (FID) while retaining the same RPrecision
and Multi-Modality performances.

###### Keywords:

Human Motion Generation AI Alignment Deep Learning

**footnotetext: Authors contributed equally.

##  1 Introduction

Synthesizing realistic human behavior is a fundamental challenge in computer
animation, holding significant relevance in gaming, film, and virtual reality
contexts. Recent advancements have shifted towards text-driven generation
methods, aiming to bypass time-consuming traditional modeling processes
requiring specialized equipment and artists’ domain knowledge. Instead,
leveraging natural language descriptions provides sufficient semantic details
to describe generic human motion. One key advantage of text-driven generative
models is their probabilistic nature, allowing for multiple diverse
generations from the same prompt, each characterized by unique nuances. Yet, a
high level of generative diversity also introduces the risk of producing
motions that are either unrealistic or deviate significantly from the intended
ones. To our knowledge, no research has addressed this aspect so far.

Figure 1: By fine-tuning the models on a synthetic preferential dataset, we
enhance the realism of generated motions. The left showcases MoDiPO’s motion
walking naturally, avoiding specific areas. Similarly, on the right, the jump
appears more natural compared to the unaligned model’s generation.

Recently, [5, 1] introduced alignment methodologies allowing users to instill
desired behaviors in pre-trained generative models by leveraging curated sets
of human preferences. This approach has succeeded in various tasks, including
question answering [18], dialogue support, and even image generation [32]. Of
particular interest, synthetic or AI-generated feedback not only circumvents
the time and cost associated with traditional human-annotated data collection
methods but also scales up the dimensions of preference datasets. Despite
substantial efforts in developing text-driven 3D human motion generative
models, our research stands out as the first to explore alignment techniques
for this task.

In order to exploit the creativity of the generative pipeline, we would like
to bias our model toward high-quality motions, avoiding altogether regions of
the learned latent manifold that lead to unfeasible motions. We base our work
on the adaptation of Direct Preference Optimization [24] for DDPMs [31] to
directly optimize the models on the preferential data. For this purpose, we
introduce “Pick-a-Move”, a dataset designed to capture human preferences for
motion. To achieve this, we utilize motions generated by SOTA text-to-motion
models. These motions are then paired with preference scores provided by a
text-to-motion retrieval model [8, 21]. These models operate within a shared
latent space, where related text and motion pairs are positioned closer
together. This shared space allows the retrieval model to express preferences
for specific text-motion combinations. We use Pick-a-Move to align text-driven
diffusion-based generative models [30, 4] for motion synthesis. Specifically,
MLD [4] is selected as it strikes a compromise between efficiency and realism,
the latter witnessed by the Frechet Inception Distance (FID).

This approach might penalize realistic and high-quality motions that do not
perfectly align with the input text. Note that training models solely on pre-
defined motion-preference pairs can restrict the model’s diversity. For this
reason, Pick-a-Move provides more flexibility in training by offering up to
$N$ motion options for each descriptive text. These motions are ranked from
most to least preferred. This allows training on pairs of text and motion
where the selection of winner and loser motion can be adjusted during the
training process.

Additionally, we exploit the availability of ground truth motions associated
with the input text by selecting these motions as winners with a low
probability: this mitigates both the risk of overfitting on training data and
the artifacts or motion-text misalignments introduced by training on generated
sequences. As a result, this supervised fine-tuning element within our
pipeline further enhances the quality of the generated outputs.

Pioneering the combination of text-driven motion generation and alignment, we
perform extensive evaluations on two datasets with two different models. We
achieve improvements in FID of up to $39\%$ while retaining consistent
RPrecision and MultiModality performances. To summarize, our contributions are
the following.

  * •

We propose the first DPO-based framework for aligning text-to-motion
generative models.

  * •

We introduce Pick-a-Move, a motion-preference dataset annotated leveraging
synthetic feedback.

  * •

We conduct an extensive experimental evaluation and ablation study to devise
the best practices for a successful alignment in text-to-motion generation.

##  2 Related Works

###  2.1 Aligning Models with Human Feedback

Early applications of models alignment employed a complex reinforcement
learning pipeline, requiring preferential data built through human feedback
(RLHF) [5]. This technique has been applied to text generation tasks such as
summarization [29]. Advancements in the reinforcement learning pipeline by
InstructGPT [19], such as the use of Proximal Policy Optimization [27], have
enabled the finetuning of models for tasks requiring evidence-supported
question answering [18] and dialogue support [7]. Several solutions have been
proposed to simplify this complex pipeline: Implicit Language Q-Learning
(ILQL) [28] utilizes Q-learning to learn value functions that guide language
model generation to maximize user-specified utility functions. Similarly, HIVE
[36] leverages offline reinforcement learning for instruction editing
alignment. Direct Preference Optimization (DPO) [24] offers a reinforcement
learning-free approach. It optimizes the model directly using a supervised
classification objective on the preferential data, eliminating the need for an
explicit reward model. This DPO approach has inspired several RL-free methods
for text-to-image alignment[16] including Diffusion-DPO [32]. Diffusion-DPO
specializes the DPO objective for DDPMs [10], a popular choice for text-driven
human motion generative models. For this reason and its simplicity, we have
adopted this latest approach.

###  2.2 Aligning Models with Synthetic Feedback

Recent works have focused on the possibility of replacing human annotators
with Synthetic Feedback (aka AI Feedback) to avoid the high costs and effort
required to collect high-quality datasets. One approach involves self-
supervision (self-improvement), as demonstrated in [1]. In this method, human
“supervision" only defines a list of prompts, that the generative model should
respect. The model then self-evaluates the generated sentences by computing a
reward based on these human-specified guidelines. This synthetically labeled
dataset is then used to train a preference model, which a policy aims to
maximize using an RL algorithm. The approach in [13] utilizes synthetic
ranking by using different models with varying levels of complexity to
generate sentences based on the same input prompt, where the outputs from
models with higher parameter counts, which tend to generate better content,
are assigned higher rewards and, thus, a higher rank. Similar techniques have
been applied to text-to-image generation, as seen in [2]. Additionally, [15]
demonstrated through extensive experiments that RLAIF (Reinforcement Learning
from AI Feedback) can be comparable to, or even outperform, RLHF. For these
reasons, we utilize synthetic feedback in our pipeline. We leverage a
retrieval model that measures the alignment between the produced motion and
the input text to rank the generated motions.

###  2.3 Text-to-Motion

Early approaches like TEMOS [20] directly used VAEs to generate motion based
on textual conditioning. Currently, two leading generation strategies
dominate. Autoregressive methods [23], such as MotionGPT [12] and T2M-GPT
[33], and Denoising Diffusion Probababilistic Models (DDPMs) [10]. The latter
category includes models like MDM [30] and MLD [4]. MDM applies DDPM directly
on raw motion data to capture the motion-text relationship for a specific
number of frames. MLD, instead, improves performances by utilizing a two-step
approach: First, they learn a compact motion latent space using VAEs; then,
they apply a diffusion process on the learned latent space leveraging Latent
DDPMs [25]. Our focus lies on improving DDPM-based models, specifically MLD,
due to their significantly reduced training and inference times compared to
other Diffusion-based approaches. Furthermore, Retrieval-Augmented Generation
[17, 35] demonstrates performance improvements when conditioning motion
generation on a sample retrieved from the entire training set. However, this
approach requires storing and searching a large database, the quality of which
significantly impacts the generation. Conversely, aligning a model does not
introduce additional computational or spatial complexity.

##  3 Background

Given our aim to enhance pre-trained motion diffusion models using the DPO
strategy, in this section we offer an overview of motion DDPMs, and their
latent counterparts. Notice that in our work we follow [8] and represent a
motion sequence as
$\mathbf{p}=\\{\mathbf{p}_{k}\\}_{k=1}^{F}\in\mathbb{R}^{F\times V}$ where $F$
is the number of frames and $V$ represents the pose vector’s features.

In Sec. 3.1 we present an overview on latent human representation, which is a
mandatory requirement for latent diffusion models. In Sec. 3.2 and in Sec. 3.3
we briefly describe the DDPMs and latent-DDPMs frameworks.

###  3.1 Latent Human Representation

VAEs consist of an encoder-decoder generative architecture trained to minimize
the reconstruction error. We employ it to reduce the pose vector $V$
dimensionality, projecting onto a manifold of feasible poses. In this
framework, the encoder network, parameterized by $\phi$, generates lower-
dimensional embeddings $\mathbf{z}\in\mathbb{R}^{n\times D}$ as outputs based
on the input poses $\mathbf{p}=\\{{\mathbf{p}_{k}}\\}_{k=1}^{F}$. Following
VAE literature [14], $q_{\phi}(\mathbf{z}|\mathbf{p})$ approximates the true
posterior distribution of the latent space with a multivariate Gaussian with a
diagonal covariance structure:

$q_{\phi}(\mathbf{z}|\mathbf{p})=\mathcal{N}(\mathbf{z}|\mu_{\phi}(\mathbf{p}),\sigma^{2}_{\phi}(\mathbf{p})\mathbf{I}),$
(1)

where $\mu_{\phi}(\cdot)$ is the mean and $\sigma_{\phi}(\cdot)$ the standard
deviation obtained as output from the encoder. We sample from the approximated
posterior $\mathbf{z}_{i}\sim q_{\phi}(\mathbf{z}|\mathbf{p}_{i})$ using:

$\mathbf{z}_{i}=\boldsymbol{\mu}_{i}+\boldsymbol{\sigma}_{i}^{2}\odot\boldsymbol{\rho},$
(2)

where $\mathbf{z}_{i}$ is a one-dimensional vector of size $D$, and
$\boldsymbol{\rho}$ is sampled from a standard multivariate Gaussian
distribution. The transformer decoder [4, 20] parametrized by $\theta$ maps
the sampled values back to body pose representation
$p_{\theta}(\mathbf{p}|\mathbf{z})$ which may be futher processed into body
meshes with the differentiable SMPL model for visualization purposes. The
network parameters are obtained by optimizing the Evidence Lower Bound (ELBO)
objective, as described in [14].

###  3.2 DDPMs

Denoising Diffusion Probabilistic Models (DDPMs) [10] work in two stages.
First, they gradually add noise to the input data through a forward process,
which is then corrupted according to a variance schedule $\beta_{t}\in(0,1)$
for $t\in\\{1,\ldots,T\\}$, transforming any data distribution $q(x_{0})$ into
a simple prior (e.g. Gaussian). This forward process can be represented as

$q(x_{t}|x_{t-1})=\mathcal{N}(x_{t};\sqrt{1-\beta_{t}}x_{t-1},\beta_{t}\mathbb{I})$
(3)

Then, a separate reverse process also dubbed as denoising process, removes
this noise, effectively cleaning the data, and is formulated as

$p_{\theta}(x_{t-1}|x_{t})=\mathcal{N}\big{(}x_{t-1};\mu_{\theta}(x_{t},t),\beta_{t}\mathbb{I}\big{)}$
(4)

where $\mu_{\theta}(x_{t},t)$ being the trained deep neural network that
estimates the forward process posterior mean, a network that effectively acts
as a denoiser.
The loss term to optimize is thus

$Loss:=\mathbb{E}_{\epsilon\sim\mathcal{N}(0,\mathbf{I}),t}[\|\epsilon-\epsilon(\mathbf{x}_{t},t)\|_{2}^{2}]\,.$
(5)

###  3.3 Latent DDPMs

We base our analysis on the latent-DDPM frameworks [25, 4] where the diffusion
process occurs on a condensed, low-dimensional motion latent space. Contrary
to the simple DDPMs that works on raw features, here the approximated
posterior $g(\mathbf{z}_{t}|\mathbf{z}_{t-1})$ gradually converts latent
representations $\mathbf{z}_{0}=\mathbf{z}$ into random noise $\mathbf{z}_{T}$
in $T$ timesteps. Then, the reverse process gradually refines the noised
vector to a suitable latent representation $\mathbf{z}_{0}$.
Following [4, 25, 10, 6], we use the notation $\\{\mathbf{z}_{t}\\}^{T}_{t=0}$
to denote the sequence of noised latent vectors, with
$\mathbf{z}_{t-1}=\epsilon_{\psi}(\mathbf{z}_{t},t)$ representing the
denoising operation at time step $t$. Here, $\epsilon_{\psi}$ refers to a
denoising autoencoder trained to predict the denoised version of its input.
The forward and reverse processes are identical to those described in
equations 3 and 4, but they are directly applied to the latent vectors of the
VAE.
At inference, $\epsilon_{\psi}(\mathbf{z}_{t},t)$ predicts
$\hat{\mathbf{z}}_{0}$ through a series of $T$ iterative denoising steps and
the frozen decoder translates $\hat{\mathbf{z}}_{0}$ into poses $\mathbf{P}$
in a single forward pass.

##  4 Methodology

Figure 2: MoDiPO Schematics: Starting with the input prompt, we generate a
winner-loser pair, which constitutes a sample in our preferential dataset. To
do so, the reference model produces $K$ generations based on the same input
prompt. These generations are then ranked by the ranker model according to
their relevance with the textual input. From these rankings, we select both a
set of winners and a set of losers. Finally, we sample from these sets to
determine the final pair. This pair is then used to refine the unfrozen target
model using DPO.

In this section, we describe our approach to DPO-based text-to-motion
alignment. In Sec. 4.1 we introduce a synthetic dataset made of motions,
generated starting from an input prompt, motions that are also paired with AI-
preferences. This dataset is then used by the alignment framework described in
Sec. 4.2.

###  4.1 Motion Preferences Dataset

Unlike text and images, motion data often suffers from scarcity. At the same
time, a dataset with motion preferences does not exist. To address this lack,
we propose a synthetic dataset named Pick-a-Move, PaM for short. To make PaM
we generate $K$ motion, with both MLD and MDM, corresponding to a conditioning
text $c$. Then, leveraging this set of $N=2K$ motion sequences
$m=\\{m_{k}\\}^{N}_{k=1}$, we employ TMR [21] and the model proposed by Guo
[8] to compute scores $s=\\{s_{k}\\}^{N}_{k=1}$ between the motion description
and the generated motions. We use $s$ to order $m$ into
$m^{*}=\\{m^{*}_{k}\\}^{N}_{k=1}$, representing a list where motions are
presented from the most coherent with $c$, namely winner, to least, loser.
This list of ranked synthetic motion sequences mimics human preferences in
ordering motions from least to most accurate according to the prompt they were
generated from. Thanks to this dataset, we can then take a pair
$(x_{0}^{w},x_{0}^{l})$ representing a winner and a loser, such that by using
their associated scores they comply with $(x_{0}^{w}\succ x_{0}^{l}|c)$ where
c is the conditional signal corresponding to the motion description. This
process thus identify which motion within a pair better reflects the textual
description. With this dataset it is possible to achieve:

  * •

Increased Pairwise Comparisons: By generating $N=2K$ motions ($K$ per used
model), we achieve up to $\binom{N}{2}$ potential winner-loser pairs per
prompt. A high number of pairs is crucial for alignment algorithms.

  * •

Preserved Multimodality: The high number of pairs associated with each prompt
helps maintain multimodality. This prevents the alignment process from
homogenizing the generated motions, reducing issues such as mode collapse.

###  4.2 Motion Alignment Pipeline

Our alignment pipeline is built upon [31], which is applicable to both DDPM
and latent DDPM for motion synthesis. The core idea of DPO is to optimize a
conditional distribution $p_{\theta}(x_{0}|c)$, instead of a reward model
$r(c,x_{0})$ as done for RLHF approaches, while regularizing the KL-divergence
from a reference distribution $p_{\text{ref}}$:

$\max_{p_{\theta}}\mathbb{E}_{c\sim\mathcal{D}_{c},x_{0}\sim
p_{\theta}(x_{0}|c)}\left[r(c,x_{0})\right]-\beta\text{KL}\left[p_{\theta}(x_{0}|c)\|p_{\text{ref}}(x_{0}|c)\right]$
(6)

However, as stated by [31], the primary challenge in DPO for diffusion models
is that the parameterized distribution $p_{\theta}(x_{0}|c)$ is not tractable,
as it needs to marginalize out all possible diffusion paths
$(x_{1},...,x_{T})$ which lead to $x_{0}$. With a few tricks and
approximations this leads to an objective defined on the whole denoising path
$x_{0:T}$:

$L_{\text{DDPO}}(\theta)=-\mathbb{E}_{x^{w}_{0},x^{l}_{0}}\log\sigma\left(\beta{\mathbb{E}}_{{\begin{subarray}{c}x^{w}_{1:T}\sim
p_{\theta}(x^{w}_{1:T}|x^{w}_{0})\\\ x^{l}_{1:T}\sim
p_{\theta}(x^{l}_{1:T}|x^{l}_{0})\end{subarray}}}\left[\log\frac{p_{\theta}(x^{w}_{0:T})}{p_{\text{ref}}(x^{w}_{0:T})}-\log\frac{p_{\theta}(x^{l}_{0:T})}{p_{\text{ref}}(x^{l}_{0:T})}\right]\right)\
$ (7)

Intuitively, during training, the model samples points along the diffusion
path and compares the newly generated data points with the preferred and non-
preferred elements of a paired dataset. The model is trained to improve its
ability to denoise the winner motion data points compared to the loser ones,
which are discouraged, according to the used ranking model, effectively
aligning its generations with AI preferences. Consequently, the training
strategy guides the model towards generating motions that effectively match
the desired characteristics defined by the used textual descriptions. This
alignment pipeline requires two models: a reference $p_{ref}$ and a target
$p_{\theta}$ model that are identical, except for the key difference of
reference model’s parameters being completely frozen (i.e., not updated during
training). We employ different tuning strategies depending on the type of
model being used: for latent diffusion models, we only fine-tune denoisers’
parameters. This approach is efficient because it operates directly in the
latent space, eliminating the need to tune the entire diffusion network, which
is also useful not to let the whole model shift too much from its previous
behavior. On the contrary, MDM denoises the raw input sequence, which is
computationally inefficient, reason why we only fine-tune the last layers of
the diffusion network.

##  5 Experimental Evaluation

This section discusses the used evaluation metrics in Sec. 5.1 and provides a
quantitative (Sec. 5.2) and qualitative (Sec. 5.3) evaluation of our
framework, and presents the results of ablation studies conducted to assess
the contribution of different components to the overall performance.

###  5.1 Evaluation Metrics

We evaluate the generated motion sequences employing all metrics adopted in
text-to-motion literature. The R-precision assesses the model’s proficiency in
producing relevant motion sequences based on textual queries. The Matching
Score (MM-Dist) quantifies the alignment between the generated motion
sequences and the textual descriptions used to generate them. Diversity
measures the variability among the generated motion sequences, while Multi-
Modality gauges the model’s capacity to produce, starting from the same
textual description, motion sequences across diverse modalities and styles.
The Fréchet Inception Distance (FID) [9] measures the similarity between the
distribution of generated motions and the distribution of ground truth. FID is
a well-established metric [3, 6], especially in image synthesis, which has
been shown to be more consistent with the human judgment of image quality
compared to the Inception Score (IS) [26] and is used as a main performance
indicator by capturing both diversity and fidelity to the ground truth
dataset. These metrics collectively provide a comprehensive evaluation of our
model’s performance in text-conditioned motion generation.

###  5.2 Quantitative Evaluation

We conducted an extensive ablation study, described in Sec. 6, using MLD as
base model and HumanML3D [8] as main dataset. Results on HumanML3D dataset are
available in Table 1, in which we reported results on the two rankers used to
gather synthetic preferences as described in Sec. 4.1 for both MDM and MLD.
The best hyperparameter set, obtained from the ablation study on HumanML3D, is
then used to further tune models on the KIT dataset, results depicted in Table
2. Notice that we re-trained from scratch MLD on KIT due to the unavailability
of the author’s model. Therefore, for a fairer comparison with the alignment
approach we applied, in Table 2 the results reported for MLD are those related
to the model we trained from scratch. In addition, the only ranker we were
able to use for KIT is backed by Guo’s motion and text encoders due to an
incompatible data representation used by TMR.
It is worth mentioning that in all cases we obtain FID improvements while also
retaining Multi-Modality and RPrecision Top3 performances. This is important
especially because during alignment it may happen that tuned models can be
affected by mode-collapse, thing that do not occur as we can infer by the
improvement of FID and the solidity of Multi-Modality.

Table 1: Results for HumanML3D [8]. Each group results corresponds to vanilla
models, aligned models and current SOTA backed by a RAG framework. Italic is
for best results overall, while bold represents best results among pretrained
models and MoDiPO aligned ones.

Model |  Top3 $\uparrow$ |  MMDist $\downarrow$ |  Diversity $\rightarrow$ |  FID $\downarrow$ |  MM $\uparrow$
---|---|---|---|---|---
Real | $.797^{\pm.002}$ | $2.974^{\pm.008}$ | $9.503^{\pm.065}$ | $.002^{\pm.0}$ | -
MotionGPT [12] | $.778^{\pm.002}$ | $\mathit{3.096}^{\pm.008}$ | $\mathit{9.528}^{\pm.071}$ | $.232^{\pm.008}$ | $2.008^{\pm.084}$
T2M-GPT [33] | $.775^{\pm.002}$ | $3.118^{\pm.011}$ | $9.761^{\pm.081}$ | $\mathit{.116^{\pm.004}}$ | $1.856^{\pm.011}$
MotionDiffuse [34] | $\mathit{.782}^{\pm.001}$ | $3.113^{\pm.001}$ | $9.410^{\pm.049}$ | $.630^{\pm.001}$ | $1.553^{\pm.042}$
MLD [4] | $.755^{\pm.003}$ | $3.292^{\pm.01}$ | $9.793^{\pm.072}$ | $.459^{\pm.011}$ | $2.647^{\pm.11}$
Ours MLD-TMR | $\mathbf{.758^{\pm.002}}$ | $\mathbf{3.267^{\pm.01}}$ | $9.747^{\pm.077}$ | $.303^{\pm.007}$ | $2.663^{\pm.111}$
Ours MLD-GUO | $.753^{\pm.003}$ | $3.294^{\pm.010}$ | $\mathbf{9.702^{\pm.075}}$ | $\mathbf{.281^{\pm.007}}$ | $\mathbf{2.736^{\pm.111}}$
MDM [30] | $.703^{\pm.005}$ | $3.658^{\pm.025}$ | $9.546^{\pm.066}$ | $.501^{\pm.037}$ | $\mathbf{2.874^{\pm.070}}$
Ours MDM-TMR | $\mathbf{.706^{\pm.004}}$ | $\mathbf{3.634^{\pm.026}}$ | $9.531^{\pm.073}$ | $\mathbf{.451^{\pm.031}}$ | $2.822^{\pm.069}$
Ours MDM-GUO | $.704^{\pm.005}$ | $3.641^{\pm.025}$ | $\mathbf{9.495^{\pm.071}}$ | $.486^{\pm.031}$ | $2.832^{\pm.066}$
ReMoDiffuse [35] | $.795^{\pm.004}$ | $2.974^{\pm.016}$ | $9.018^{\pm.075}$ | $.103^{\pm.004}$ | $1.795^{\pm.043}$

Table 2:  Results for KIT-ML [22]. Each group results corresponds to vanilla
models, aligned models and current SOTA backed by a RAG framework. Italic is
for best results overall, while bold represents best results among pretrained
models and MoDiPO aligned ones.

Model |  Top3 $\uparrow$ |  MMDist $\downarrow$ |  Diversity $\rightarrow$ |  FID $\downarrow$ |  MM $\uparrow$
---|---|---|---|---|---
Real | $.779^{\pm.006}$ | $2.788^{\pm.012}$ | $11.08^{\pm.097}$ | $.031^{\pm.004}$ | -
MotionGPT [12] | $.680^{\pm.005}$ | $3.527^{\pm.021}$ | $10.35^{\pm.084}$ | $\mathit{.510}^{\pm.016}$ | $\mathit{2.328}^{\pm.117}$
T2M-GPT [33] | $\mathit{.745}^{\pm.006}$ | $3.007^{\pm.023}$ | $10.92^{\pm.108}$ | $.514^{\pm.029}$ | $1.570^{\pm.039}$
MotionDiffuse [34] | $.739^{\pm.004}$ | $\mathit{2.958}^{\pm.005}$ | $\mathit{11.10}^{\pm.143}$ | $1.954^{\pm.062}$ | $0.730^{\pm.013}$
MLD [4] | $.718^{\pm.005}$ | $\mathbf{3.156^{\pm.023}}$ | $10.921^{\pm.108}$ | $.733^{\pm.032}$ | $1.595^{\pm.087}$
Ours MLD-GUO | $\mathbf{.720^{\pm.006}}$ | $3.166^{\pm.03}$ | $\mathbf{11.022^{\pm.074}}$ | $\mathbf{.623^{\pm.037}}$ | $\mathbf{1.660^{\pm.068}}$
MDM [30] | $\mathbf{.726^{\pm.005}}$ | $3.098^{\pm.023}$ | $\mathbf{10.690^{\pm.088}}$ | $.496^{\pm.028}$ | $\mathbf{1.829^{\pm.037}}$
Ours MDM-GUO | $0.725^{\pm.005}$ | $\mathbf{3.097^{\pm.023}}$ | $10.681^{\pm.086}$ | $\mathbf{.450^{\pm.026}}$ | $1.821^{\pm.038}$
ReMoDiffuse [35] | $.765^{\pm.055}$ | $2.814^{\pm.012}$ | $10.80^{\pm.105}$ | $.155^{\pm.006}$ | $1.239^{\pm.028}$

MoDiPO’s main purpose is to discourage the generation of implausible motions
by improving consistency of diffusion-based text-to-motion models. While these
models can generate impressive motions, the stochasticity inherent in the
diffusion process can sometimes lead to the generation of poor-quality
motions, either affected by foot-skating or jittering, or incoherent with the
input prompt.
Aiming to show that models tuned with our MoDiPO methodology are more
consistent even in the case of multiple generations for the same prompt, we
synthesize eight different motions for each prompt of HumanML3D test set. We
then ranked these motions using the Guo Ranker, which is also used for dataset
synthetic annotation and ablation study as described in Sec. 6.2. Finally, we
compute all the used evaluation metrics exclusively for the worst and best
motion sequences from each set of eight generations.
As shown in Table 3(a) for HumanML3D and Table 3(b) for KIT-ML, the vanilla
MLD model exhibits a significant difference in FID scores between the worst
and best motions. By contrast, using MoDiPO, models significantly reduce the
difference between the FID scores for loser and winner motions. In particular,
we observe a gap reduction of 15.05% (from 0.711 to 0.604) for HumanML3D and
of 96.51% (from 0.172 to 0.006) for KIT-ML. It is worth noting that the FID
score for losers decreases from 0.997 to 0.789 (an improvement of 20.86%) for
HumanML3D and from 1.037 to 0.769 (an improvement of 25.84%) for KIT-ML.
Besides the reduced gap between loser and winner, the lower overall FID for
the aligned model suggests that MoDiPO is a practical solution for improving
the consistency of motion quality in diffusion models.

Table 3: Performances of Winner (W) and Loser (L) among the 8 generations per-
prompt of vanilla MLD (MLD) and MLD aligned with MoDiPO (Ours) for HumanML3D
and KIT-ML. The typical evaluation method calculation is used in the case of
MLD and Ours (aligned model).

(a) HumanML3D

Model |  Top3 $\uparrow$ |  MMDist $\downarrow$ |  Div. $\rightarrow$ |  FID $\downarrow$
---|---|---|---|---
Real | $.797^{\pm.002}$ | $2.974^{\pm.008}$ | $~{}9.503^{\pm.065}~{}$ | $.002^{\pm.0}$
MLD | $.755^{\pm.003}$ | $3.292^{\pm.010}$ | $9.793^{\pm.072}$ | $.459^{\pm.011}$
MLD L | $.511^{\pm.003}$ | $4.822^{\pm.014}$ | $9.249^{\pm.079}$ | $.997^{\pm.026}$
MLD W | $.914^{\pm.001}$ | $2.341^{\pm.004}$ | $9.942^{\pm.075}$ | $.286^{\pm.007}$
Ours | $.753^{\pm.003}$ | $3.294^{\pm.010}$ | $9.702^{\pm.075}$ | $.281^{\pm.007}$
Ours L | $.487^{\pm.002}$ | $4.945^{\pm.014}$ | $9.056^{\pm.069}$ | $.789^{\pm.021}$
Ours W | $.916^{\pm.001}$ | $2.303^{\pm.007}$ | $9.873^{\pm.079}$ | $.185^{\pm.005}$

(b) KIT-ML

Model |  Top3 $\uparrow$ |  MMDist $\downarrow$ |  Div. $\rightarrow$ |  FID $\downarrow$
---|---|---|---|---
Real | $.779^{\pm.006}$ | $2.788^{\pm.012}$ | $~{}11.080^{\pm.097}~{}$ | $.031^{\pm.004}$
MLD | $.718^{\pm.005}$ | $3.156^{\pm.023}$ | $10.921^{\pm.108}$ | $.733^{\pm.032}$
MLD L | $.619^{\pm.007}$ | $4.001^{\pm.034}$ | $10.829^{\pm.100}$ | $1.037^{\pm.053}$
MLD W | $.799^{\pm.006}$ | $2.672^{\pm.024}$ | $11.302^{\pm.115}$ | $.865^{\pm.039}$
Ours | $.720^{\pm.006}$ | $3.166^{\pm.030}$ | $11.022^{\pm.074}$ | $.623^{\pm.037}$
Ours L | $.615^{\pm.004}$ | $4.048^{\pm.026}$ | $10.805^{\pm.106}$ | $.769^{\pm.047}$
Ours W | $.802^{\pm.005}$ | $2.646^{\pm.022}$ | $11.297^{\pm.114}$ | $.763^{\pm.034}$

###  5.3 Qualitative Evaluation

To perform qualitative evaluation we generated motions using the best
performing model from our ablation study (Table 4). In Fig. 4 it is possible
to see qualitatives of both pre-trained MLD and the post-DPO version of MLD.
Even though it is difficult to judge movements just from pictures, it is easy
to see the improvement from these examples. In particular from the prompt "a
person walks down the stairs" of Fig. 4(a), the tuned model generates a motion
that is more aligned with a "walk down the stairs" action.
At the same time, in the case of Fig. 4(b) with the prompt "A person walks
forwards, sits", the post-DPO model better capture the "sits" movement.
In Fig. 4(c) for vanilla-MLD model the "jogging" action is performed on the
spot, while the aligned model is more coherent to the used prompt and to a
more realistic execution of movements described by it.
However, in Fig. 4(f) it is possible to see how tricky the input prompt can
be: in this case the pre-trained model generated a motion of a person walking
forward, while the post-DPO model seems to give more importance to the
"steady" part of the description, which thus outputs a motion of a person
steady walking, a movement made on the spot.

(a) A person walks down the stairs

(b) A person walks forwards, sits

(c) A person is jogging around

(d) A person is walking around in circles with their left arm on or in
something

(e) A person is sitting with both hands together

(f) A person is jogging forward in a steady manner

Figure 4: Qualitative results on HumanML3D. Vanilla MLD is represented by blue
motions, while MLD aligned with MoDiPO is represented by yellow motions.

##  6 Ablation Studies

We conducted a series of ablation studies to analyze the impact of specific
choices within the proposed method. In Sec. 6.1, we investigated the effects
of using stochastic or edge sampling of winner-loser pairs for the ranking
process. Sec. 6.2 covers the evaluation of performances for different ranking
methods used within the framework. In Sec. 6.3, there is a description of the
advantages and disadvantages of using motions generated by models other than
the model we aim to align. Finally, Sec. 6.4 illustrates an online alignment
experiment.

###  6.1 Pair Selection

With the dataset described in Sec. 4.1, we choose two strategies of winner-
loser selection: edge and stochastic selection. In the edge selection, we just
take hard winners and hard losers from the ranked list of motion sequences.
For the stochastic selection, instead, we divided the list into two parts of
which the first half contains winners, while the second half includes losers.
According to our experiments, as can be seen in Table 4, this second strategy
performs better if compared to the edge selection.
We suppose that the model, subjected to different generations for the same
textual prompt, retains its R-Precision and Multi-Modality performances while
also reducing the FID thanks to alignment with DPO.
We also tried to substitute the winner, with a probability of $0.25$ or $0.5$,
with the ground truth motion as additional supervision to further enhance the
possibility of generating more realistic motions. However, as depicted in
Table 4, even if this setting helps decreasing FID and increasing Multi-
Modality, it deteriorates RPrecision performances.

###  6.2 Ranking Method

As described in Sec. 4.1, we propose to synthetically rank generated motions
starting from two models: TMR and the motion and text encoders proposed in
[8], which we will dub as Guo. While TMR has been proposed to tackle retrieval
tasks, Guo was introduced for evaluation purposes. For both the used datasets,
KIT and HumanML3D, we annotated each set composed of text motions with Guo.
Instead, TMR was used only for HumanML3D annotation. This is mainly due to a
mismatch in the KIT data representation, which was updated to the SMPL-like
representation in the case of TMR. This made it impossible for us to use it in
KIT synthetic ranking, knowing that the motions generated by MLD and MDM have
a parameter mismatch with this updated representation. Results of experiments
done with both the used rankers are available in Table 4.

###  6.3 Alignment from model’s own generations

As described in Sec. 4.1, we used synthetically annotated datasets generated
by MLD and MDM models. We hypothesized that incorporating motions generated by
MDM during MLD tuning could offer potential benefits. Indeed, a greater amount
of winner-loser pairs help maintain multimodality and R-Precision performance,
as previously observed. At the same time, utilizing motions from both models
could expose the target model to different approaches for generating good
motions based on the textual prompt. However, as shown in Table 4, this
approach did not yield the expected improvements. The performance of the
target model decreases if compared to using only its own generated motions for
tuning.

###  6.4 Online Alignment

We explored an alternative approach using online alignment with the MLD model.
This approach is feasible due to MLD’s latent-space operation, which
significantly reduces the time required to generate output motions.
In this scenario, the frozen reference model generates motions which are then
ranked and from which we selected winner-loser pairs using the stochastic
selection. This entire process occurs online, offering potential benefits in
terms of efficiency and adaptability.
However, initial results show a trade-off between different metrics. While the
target model’s FID decreases, suggesting improved quality in distribution
similarity, the R-Precision Top3 metric also decreases. This suggests that for
each winner-loser pair more iterations are necessary to let the target model
effectively repulse loser motions and attract winner ones.

Table 4: Ablation study with MLD model on HumanML3D dataset [8]. Stoch stands
for stochastic selection of pairs, default is edge selection. $GT_{p}$ is the
probability that there is supervision with the ground truth sequence used at
the spot of winner in a pair. Online refers to the generation and ranking, on
the fly, of sequences generated by the reference model. PaM+ stands for Pick-
a-Move dataset used in its entirety, meaning that generations of both MLD and
MDM are used for the winner-loser pair selection. Reported evaluation metrics
are RPrecision Top3, MMDistance, Diversity, FID and Multi-Modality.

Scorer | Stoch. | $GT_{p}$ | Online | PaM$+$ | Top3 $\uparrow$ | MMDist $\downarrow$ | Diversity $\rightarrow$ | FID $\downarrow$ | MM $\uparrow$
---|---|---|---|---|---|---|---|---|---
without alignment | $.755^{\pm.003}$ | $3.292^{\pm.010}$ | $9.793^{\pm.072}$ | $.459^{\pm.011}$ | $2.647^{\pm.110}$
Guo | $\checkmark$ |  |  |  | $.753^{\pm.003}$ | $3.294^{\pm.010}$ | $9.702^{\pm.075}$ | $.281^{\pm.007}$ | $2.736^{\pm.111}$
TMR | $\checkmark$ |  |  |  | $.758^{\pm.002}$ | $3.267^{\pm.010}$ | $9.747^{\pm.077}$ | $.303^{\pm.007}$ | $2.663^{\pm.111}$
Guo |  |  |  |  | $.752^{\pm.003}$ | $3.300^{\pm.010}$ | $9.714^{\pm.077}$ | $.336^{\pm.009}$ | $2.736^{\pm.110}$
TMR |  |  |  |  | $.759^{\pm.002}$ | $3.262^{\pm.010}$ | $9.714^{\pm.079}$ | $.325^{\pm.007}$ | $2.630^{\pm.107}$
Guo | $\checkmark$ | .25 |  |  | $.745^{\pm.002}$ | $3.324^{\pm.010}$ | $9.674^{\pm.077}$ | $.261^{\pm.007}$ | $2.834^{\pm.119}$
Guo | $\checkmark$ | .5 |  |  | $.745^{\pm.003}$ | $3.327^{\pm.010}$ | $9.614^{\pm.076}$ | $.273^{\pm.007}$ | $2.826^{\pm.117}$
Guo | $\checkmark$ |  | $\checkmark$ |  | $.677^{\pm.003}$ | $3.701^{\pm.013}$ | $9.241^{\pm.079}$ | $.276^{\pm.008}$ | $3.477^{\pm.144}$
Guo | $\checkmark$ | .25 | $\checkmark$ |  | $.714^{\pm.003}$ | $3.496^{\pm.010}$ | $9.489^{\pm.074}$ | $.293^{\pm.009}$ | $3.179^{\pm.128}$
Guo | $\checkmark$ |  |  | $\checkmark$ | $.761^{\pm.003}$ | $3.252^{\pm.010}$ | $9.851^{\pm.071}$ | $.335^{\pm.008}$ | $2.610^{\pm.110}$
TMR | $\checkmark$ |  |  | $\checkmark$ | $.759^{\pm.002}$ | $3.266^{\pm.010}$ | $9.798^{\pm.073}$ | $.345^{\pm.007}$ | $2.592^{\pm.104}$

##  7 Limitations

While our study introduces the first alignment framework for text-driven
generative models for human motion generation, there are several limitations
that require consideration. In our approach, we fine-tune the entire denoiser
for Motion Latent Diffusion (MLD) and the last layers of Motion Diffusion
Model (MDM), which may not be optimal as it could underperform if compared to
other fine-tuning strategies such as LoRA [11], or fine-tuning the whole
model. In the future, we aim to employ parameter efficient fine-tuning (PEFT)
strategies such as LoRA and its variants for more computation-intensive models
such as MDM.

##  8 Conclusions

We have presented the first framework designed for aligning text-to-motion
generative models. Our approach significantly enhanced the aesthetics of
motion generation, as demonstrated through both qualitative and quantitative
analyses, showcasing improvements of up to $39\%$ on the Fréchet Inception
Distance (FID). Utilizing AI-feedback, we constructed a preferential dataset,
augmenting its diversity by introducing stochasticity in the selection process
of winner-loser pairs. Leveraging the training dataset enabled us to explore
innovative strategies, such as incorporating ground-truth motion, further
enhancing the model’s adherence to the underlying data distribution.

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# PDOZ: innovative personal electronic dosimeter for electron, gamma and
neutron H∗(d) dosimetry

Lucia Salvi⋆,1,2,3, Giulia Rossi1,2, Giovanni Bartolini1,3, Ali Behcet Alpat1,
Arca Bozkurt4, Mustafa Dogukan Cegil4, Ahmet Talha Guleryuz4 ⋆ Corresponding
author  1 Istituto Nazionale di Fisica Nucleare (INFN), Section of Perugia,
Perugia, Italy  2 University of Perugia, Department of Physics and Geology,
Perugia, Italy  3 BEAMIDE srl, Via Campo di Marte $4/$O, $06124$, Perugia,
Italy  4 IRADETS A.S., Teknopark Istanbul, Pendik/Istanbul, Turkiye
<EMAIL_ADDRESS>
###### Abstract

The personal (or active) electronic dosimeters (PEDs) are devices used to
determine the individual exposure to ionizing radiations and they are employed
in hospitals, research laboratories and nuclear power plants. The PDOZ project
is a personal electronic dosimeter able to detect, discriminate and measure
the delivered dose by beta particles, gamma rays and neutrons. In this paper,
several Monte Carlo simulations are described. The first one is regarding the
ICRU sphere, [1], implemented to evaluate the ambient dose equivalent, H*(10),
and the conversion factors for gamma rays and beta particles. The second
simulation is carried out to study the prototype dosimeter response to gamma
rays and beta particles and, also thanks to previous one, to obtain the
conversion curve necessary to calculate the ambient dose equivalent from the
silicon photomultipliers counts. In the last one, instead, the performance of
a prototype dosimeter, composed by a small plastic scintillator coupled to two
SiPMs, is evaluated and a simulation with different radioactive sources is
made whose results are compared with the experimental measurements. All
simulations are carried out by Geant4 including the optical photon transport.

Keywords: dose, dosimeter, fluence, Geant4, PDOZ, scintillator, SiPM, ambient
dose equivalent, ICRU, conversion factors, H*(10)

##  1 Introduction

In recent years, dosimetric measurements in the various fields of application
of ionizing radiation have become increasingly necessary. Nuclear
applications, in fact, are not only for electrical power generation or medical
applications concerning diagnostic imaging and radiotherapy or hadrontherapy
treatments. Ionizing radiation is also used for sterilization of medical and
pharmaceutical products and for irradiation of food to improve its
preservation for long periods of time. Simultaneously with these applications,
dosimetric systems have been developed to control radiation processes and
determine the amount of energy released from radiation into matter [2].
Furthermore, the radiation received by exposed people during and after
catastrophic events like Fukushima, Chernobyl or in a radiological accident
must be accurately measured. The precision and reliability of the measurement
even in this harsh radiation environment situations are of paramount
significance for decision making after such an unfavorable event and on
protective action [3]. These events have shown that most of state of the art
of commercial PEDs show their limitations in particular in linearity of their
response to wide energy mixed radiation fields (i.e. electrons, photons and
neutrons). We design PDOZ, that will use both organic and inorganic
scintillators, to be a reliable PED with linear response in mixed fields of
radiation of wide energy ranges. A non - exhaustive list of applications of
PDOZ can be as: in medical imaging well logging, homeland security, marine and
space exploration, and high energy physics (HEP).
Nowadays, there are many different dosimetric methods, each of which provides
information on the energy and dose absorbed by the medium on which the
ionizing radiation impacted.
Personal dosimeter currently on the market can detect gamma rays and neutrons;
gamma rays and thermal and fast neutrons; gamma rays and beta particles;
gamma, X - rays and neutrons. For example the EPD - N2 dosimeter, developed by
Thermo Fisher Scientific [4], can detect gamma radiation (and also x - rays)
and thermal neutrons in the energy ranges $20$ $KeV$ \- $10$ $MeV$ and $0.025$
$eV$ \- $15$ $MeV$ respectively with an energy response ranging from $\pm
20\%$ to $\pm 50\%$ for gammas (it depends on the energy) and $\pm 30\%$ for
neutrons. Other example to personal electronic dosimeters with multi -
detector capabilities are the NRF series, namely NRF30, NRF31 and NRF34,
developed bu FujiElectric [5]. The NRF30 can detect gamma and X - ray in the
energy range from $30$ $KeV$ to $6$ $MeV$. The NRF31 instead can detect both
gamma (X) - rays and neutrons in the energy ranges $30$ $KeV$ \- $6$ $MeV$ and
$0.025$ $eV$ \- $15$ $MeV$ respectively. In the end, the NRF34 can detect
gamma (X) - rays and beta particles in the energy ranges $30$ $KeV$ \- $6$
$MeV$ and $0.2$ $MeV$ \- $0.8$ $MeV$ (mean energy). For all of them the energy
response is $\leq\pm 20\%$ for gamma (X) - rays, $\leq\pm 30\%$ for beta
particles and $\leq\pm 50\%$ for neutrons. None of these personal electronic
dosimeters can detect gamma - rays, beta particles and neutrons at the same
time.

The PDOZ is a project consisting in a dosimeter development that can detect
and discriminate three different kinds of particles: beta, gamma and neutrons.
For this purpose three scintillators, a plastic one and two distinct crystals,
are employed and two silicon photomultipliers, SiPMs, are placed under the
bottom surface of each of them. Each scintillator is specific to one type of
particle to be detected: the plastic one is employed to measure the dose
delivered by beta particles, whereas the two crystals are used to individually
measure the dose delivered by gamma particles and neutrons. The silicon
photomultipliers are located in the bottom side of the scintillators in order
to detect the light produced when a particle enters inside them and releases
some energy. This energy excites the scintillator atoms to luminescence and
during their return to ground state they emit light photons, in our case
wavelength in blue light region, which are then collected by silicon
photomultipliers. Scintillators play a crucial role radiation detection
material. They indirectly detect radiation and are usually coupled with a
photo - sensor that reads the energy deposited in scintillator which are
converted into light photons. Scintillators are classified into organic and
inorganic, and the scintillator type used in a radiation detector is
determined by the type of radiation particle to be measured as well as the
purpose of radiation detection. Plastic scintillators are organic
scintillators while inorganic scintillators are primarily ionic solids and
composed of high - density crystals. Inorganic scintillators can then be
classified into two categories, single - crystals and polycrystalline
ceramics, with the former typically exhibiting better optical properties at
the expense of fabrication costs [6], [7].
The electronic circuit is implemented to consider the light as a signal when
both the SiPMs have a pulse over threshold in coincidence. When a coincidence
occurs it is interpreted as a count in the device. Compared to traditional
PhotoMultiplier Tube (PMT) sensors, small sized SiPMs sensors are widely used
in personal dosimeters, have lower operating voltages and consume less power.
PDOZ will have several dosimetry applications where the user can observe the
real time dose and the dose deposited by each type of particle. It can be used
in various places, for instance hospitals, research centers, nuclear power
plants, laboratories and in every environment where radiations are present.
In this work, the study of the fluence to ambient dose equivalent curve, the
dosimeter response to gamma and beta particles and the conversion curves are
described in the ICRU simulation and single dosimeter response simulation. In
the end, the performance study of a single dosimeter with different
radioactive sources is carried out, and the results are compared and validated
with experimental data.

##  2 Materials

The PDOZ dosimeter will be able to measure the absorbed dose released from
different kinds of sources. For this reason, the final version includes three
separate scintillators:

  * •

plastic scintillator, the BC408 [8], for beta particles;

  * •

crystal, CsI(Tl) [9], for gamma rays;

  * •

another $10$B or $6$LiF coated crystal, (to be decided), for neutrons.

The three scintillators are put at the same height inside the PEDs external
box together with their electronic circuit for the detection. Coupled to the
bottom of each scintillator there are two silicon photomultipliers, SiPM: ASD-
NUV1C-P [10], to detect the light produced by entering particles. Figure 1
shows the device with the three scintillators.

Figure 1: Geometry of the PDOZ. The scintillators are in purple, blue and
green, whereas the SiPMs, two for each scintillator, are in red.

To study the performance of a single scintillator dosimeter (using BC408)
three calibrated laboratory radioactive sources have been used to collect
data:

  * •

${}^{90}Sr$ having an activity $A=\left(3.7\pm 20\%\right)$ $kBq$ and half -
life $\tau_{1/2}=28.98$ years;

  * •

${}^{60}Co$ with an activity $A=\left(37\pm 5\%\right)$ $kBq$ and half - life
$\tau_{1/2}=5.27$ years;

  * •

${}^{137}Cs$ having an activity $A=\left(33\pm 20\%\right)$ $kBq$ and half -
life $\tau_{1/2}=30.08$ years.

The simulations of the ICRU sphere and those carried out to study the response
of a single scintillator to gamma and beta particles and to the radioactive
sources are implemented thanks to the Geant4 [11] toolkit, that is used to
create simulations of particles and radiation passage through the matter and
any kind of setup or detector.

##  3 Conversion curves calculation

###  3.1 Definitions of ICRU sphere and H*(10)

The definitions of ICRU sphere and ambient dose equivalent, H*(10), employed
are the ones provided by the International Commission on Radiological
Protection. The ICRU sphere is a sphere with unity density, $1$ $g/cm^{3}$, a
diameter of $30$ $cm$ and made of tissue-equivalent material, so $76.2\%$
oxygen, $11.1\%$ carbon, $10.1\%$ hydrogen, $2.6\%$ nitrogen [1] and serves to
validate Monte Carlo simulations used to trace the conversion curve from
count/time reading to ambient dose equivalent. Figure 2 illustrates the ICRU
sphere simulation.

Figure 2: Monte Carlo simulation of a parallel gamma rays beam at $100$ $KeV$,
impinging on a ICRU sphere where different interactions take place.

The H*(10), instead, is: "the ambient dose equivalent at a point in a
radiation field is the dose equivalent that would be produced by the
corresponding expanding and aligned field in the ICRU sphere at a depth of
$10$ $mm$ on the radius vector opposing the direction of the aligned field
[12]".

###  3.2 ICRU Simulations

To calculate the conversion factors from fluence to ambient dose equivalent
both for gamma and beta particles, Monte Carlo simulations are implemented
with Geant4. An ICRU sphere is simulated together with a sensitive volume
composed by a tissue-equivalent cube having dimensions $1\times 1\times 1$
$mm^{3}$ and placed at a depth of $10$ $mm$ on the radius vector opposing the
direction of the aligned field for the particles. The source distribution is
peaked on the axis where the cube is placed in order to reduce the simulation
time without decreasing the statistic. The events are generated according to
Equation 1, [13],

$r=R\cdot\xi^{\frac{1}{1-\alpha}}$ (1)

in which $r$ is the radial coordinate, $R=15$ $cm$ represents the beam radius,
$\xi\in\left(0,1\right)$ stands for a random number and $\alpha$ indicates a
constant parameter set at $0.5$ as reported in the article [13]. The scored
quantities must be weighted with the statistical weight $w$ defined in
Equation 2.

$w=\frac{2}{1-\alpha}\cdot\frac{r^{1+\alpha}}{R^{1+\alpha}}$ (2)

Several beams of $10^{7}$ monoenergetic gamma rays are generated with a flat
energy ranging distribution from $0$ $KeV$ to $2000$ $KeV$.

The same procedure is then applied to beta particles. Since electrons are low
penetrating particles, the ambient dose equivalent, H*(d), is calculated at a
depth of $d=0.07$ $mm$ as it is recommended by the ICRP standard for low
penetrating radiations [14]. For this reason, the geometry is changed and a
box of $0.01\times 0.01\times 0.01$ $mm^{3}$ is placed at a depth of $0.075$
$mm$. In this case $10^{7}$ monoenergetic beta particles are generated with
the energy ranging from $100$ $KeV$ to $5000$ $KeV$.

In every simulation, for each energy, the absorbed dose in the ICRU box is
recorded. Figure 3 shows the dose in the ICRU box volume.

Figure 3: The dose deposited in ICRU box for gamma particles in red and for
beta particles in blue.

###  3.3 Fluence to ambient dose equivalent

To calculate the conversion factors, the fluence is determined with Equation 3

$F=\frac{N}{A}$ (3)

in which $F$ is the fluence measured in $cm^{-2}$, $N$ stands for the number
of generated events and $A$ represents the area where the source is generated
which is a circle of radius $2$ $cm$. The source radius is now set to $2$ $cm$
as the dosimeter dimensions are smaller than those of the ICRU sphere. The
conversion factors are found with Equation 4

$X=\frac{D}{F}$ (4)

where $X$ is the conversion factor measured in $pSv\cdot cm^{2}$ for gamma
rays and in $nSv\cdot cm^{2}$ for beta particles, $D$ represents the dose and
$F$ indicates the fluence. Figure 4 and Figure 5 report the results.

Figure 4: In the first picture, the comparison between the conversion
coefficients from our simulation and the ICRP74 values for gamma particles. In
the second one the same comparison for the beta particles.

Figure 5: In the first picture, the ratio between the conversion coefficients
from the simulation and the ICRP74 values for gamma particles; in the second
one, the ratio between the conversion coefficients from simulation and ICRP74
values for beta particles.

###  3.4 Plastic scintillator dosimeter simulation

In order to study the performance of a single dosimeter, the device energetic
and geometrical efficiencies when subjected to different types of radiation
are simulated. The incoming particle hits the scintillator, the energy
deposited in it excites the scintillator molecules which then release some
energy in form of optical photons. The wavelength of the optical photon
released by BC408 in use is peaked around $420$ $nm$ where the coupled SiPM’s
quantum efficiency is at its maximum. To evaluate the dose, the conversion
factors, from the count per seconds to $Sv/h$, are obtained by studying the
dosimeter response to different kinds of ionising radiation. The simulation
geometry employed has to match that of the experimental prototype, so it
involves a $10\times 5\times 15$ $mm^{3}$ plastic scintillator, the BC408, two
holes for the silicon photomultipliers and their cables and a $100$ $\mu m$
foil of teflon wrapping to avoid optical photons to escape from scintillator.
In order to reproduce the behaviour as realistic as possible, the photon
detection efficiency of the silicon photomultipliers is taken into account.
Figure 6 shows the simulation of the single dosimeter geometry simulation and
the experimental device.

Figure 6: In the left picture the Geant4 dosimeter simulation: in grey the two
holes below for SiPMs and their cables, in blue the teflon foil. In the right
image the experimental device with plastic scintillator.

Three different simulations are implemented with three different acquisition
system settings:

  * •

p.e.0, all the coincidences (any number of photons hitting two SiPMs in
coincidence) are considered;

  * •

p.e.1, the first photoelectron peak is eliminated from the coincidens counting
(when only one optical photon is detected by both the SiPMs);

  * •

p.e.2, both the first and second photoelectron peaks are removed from the
coincidence counting.

####  3.4.1 Gamma particles simulation

A single dosimeter, with a BC408 scintillator, is simulated with a circle-
shape source having a radius, $\left(r\right)$, of $1$ $cm$ and $10^{5}$
events are generated with the energy ranging from $100$ $KeV$ to $2500$ $KeV$.
Equation 5 is the fluence, in $cm^{-2}$, used to normalize the quantities:

$F=\frac{n}{\pi r^{2}}=\frac{10^{5}}{\pi}$ (5)

where $F$ represents the fluence, $n$ stands for the number of events and $r$
is the radius. The dosimeter response, necessary to find the ambient dose
equivalent from the SiPMs counts, is given by Equation 6

$R\left(E\right)=\frac{n_{c}}{F}$ (6)

in which $R\left(E\right)$ is the response, $n_{c}$ indicates the number of
events with two SiPMs in coincidence and $F$ stands for the fluence. Figure 7
shows the dosimeter response in the three different settings.

Figure 7: Number of two SiPMs signal coincidences normalized to the fluence
for the p.e.0, p.e.1 and p.e.2 threshold settings in red, blue and green,
respectively.

The conversion curve, in $\mu Sv/CPS\cdot h$, is estimated with Equation 7

$CF=\frac{X}{R}$ (7)

where $CF$ is the conversion factor, $X$ stands for the fluence to ambient
dose equivalent curve obtained from the ICRU simulation and converted in $\mu
Sv\cdot cm^{2}$ and $R$ represents the response of the dosimeter. The
conversion curve for the ambient dose equivalent can be estimated with
Equation 8, [15],

$f\left(E\right)=\sum_{k=1}^{K_{max}}A\left(k\right)\left(\log E\right)^{k-1}$
(8)

where $A\left(k\right)$ represents a parameter, $K_{max}$ is the total number
of $A\left(k\right)$ terms and $E$ stand for the energy.
Figure 8 illustrates the conversion curves for gamma particles fitted with
Equation 8 in the three settings.

Figure 8: Gamma event conversion curves for the p.e.0, p.e.1 and p.e.2
threshold settings, in red, blue and green, respectively.

####  3.4.2 Beta particles simulation

The same procedure described before is applied with a beta particles source in
which $10^{5}$ events are generated with energy ranging from $100$ $KeV$ to
$2500$ $KeV$. Figure 9 illustrates the dosimeter response in the three
settings, whereas Figure 10 shows the conversion curve for beta particles
fitted with Equation 8.

Figure 9: Number of coincidences normalized to the fluence for the p.e.0,
p.e.1 and p.e.2 threshold settings in red, blue and green, respectively.
Figure 10: Beta event conversion curves for the p.e.0, p.e.1 and p.e.2
threshold settings, in red, blue and green, respectively.

##  4 Results and Discussion

###  4.1 Source simulations and data analysis

In order to study the performance of one dosimeter with a single scintillator,
several simulations are carried out with distinct sources whose activities are
corrected taking into account the elapsed time, and, subsequently, the results
are compared with the experimental data. The experimental set up involves
different settings with the distance between the dosimeter and the source
varying. Table 1 shows the data sets taken with all the sources employed and
the distances between the source and the dosimeter.

Table 1: Data sets taken with the sources and the distances Source | Distances [cm] | Source | Distances [cm] | Source | Distances [cm]
---|---|---|---|---|---
${}^{90}Sr$ | 1 | ${}^{60}Co$ | 1 | ${}^{137}Cs$ | 1
| 2 |  | 2 |  | 2
| 3 |  | 3 |  | 3
| 4 |  | 4 |  | 4
| 5 |  | 5 |  | 5

The simulation geometry consists of a single plastic scintillator, BC404 with
dimensions $10\times 5\times 15$ $mm^{3}$, on which a foil of teflon, $100$
$\mu m$ thick, is placed. Also the source geometry is implemented in order to
make comparisons with experimental data. The radioactive source is placed
inside a disk of plexiglass and epoxy. The SiPMs are coupled to scintillator
with EPO-TEK EJ2189 electrically conductive two-component epoxy glue [16].
Figure 11 shows the experimental set up simulation.

Figure 11: Geometry of the plastic scintillator with two holes of depth $5$
$mm$ each in which two SiPMs are inserted and geometry of the source. The red
disk is made of plexiglass whereas the blue one of epoxy.

The sources employed are ${}^{90}Sr$, ${}^{60}Co$ and ${}^{137}Cs$ [17] that
have the following decays

${}^{90}Sr\rightarrow^{90}Y+e^{-}+\bar{\nu}_{e}$
${}^{60}Co\rightarrow^{60}Ni+e^{-}+\bar{\nu}_{e}+\gamma_{1}+\gamma_{2}$

with $\gamma_{1}=1.173$ $KeV$ and $\gamma_{2}=1.332$ $KeV$,

${}^{137}Cs\rightarrow^{137}Ba+e^{-}+\bar{\nu}_{e}+\gamma$

in which $\gamma=661$ $KeV$. The sources are used to study the dosimeter
detection of gamma rays and beta particles. Figure 12 illustrates their
spectra.

Figure 12: In the first picture the ${}^{90}Sr$ spectrum, in the second one
the ${}^{60}Co$ spectrum whereas in the last image the ${}^{137}Cs$ spectrum.
The beta spectrum is in green, the gamma one in red whereas the total spectrum
is in blue.

To simulate the device behaviour, also the Photon Detection Efficiencies of
the SiPMs are considered. One count is given when there is the coincidence
between both SiPMs signals. The settings used to make the comparison between
simulated and experimental data are the same described in section 3.4.
Figure 13 shows the comparison between the simulated and the experimental data
for the three different sources and settings.

Figure 13: In the first picture the comparison between simulated, in magenta,
red and dark cyan, and experimental data, in dark green, blue and lilac,
respectively for the p.e.0, p.e.1 and p.e.2 settings for the ${}^{90}Sr$
source. In the second one for the ${}^{60}Co$ source, whereas in the last
image for the ${}^{137}Cs$ source.

##  5 Conclusions

In this work, the ICRU procedure suggested in [13] has been followed to obtain
the ambient dose equivalent and the conversion factors for gamma rays and beta
particles sources. The same simulation is then implemented on the detector in
order to study the performance of a single scintillator seen by two SiPMs when
it is exposed to gamma ray or beta particle sources. Main goal of this study
is to validate our Geant4 simulation of a single scintillator personal
dosimeter (PED) following the procedure suggested by ICRU. Our PED provides
coincident event counts for various configurations. The simulation creates the
exact same configuration of the real experimental setup and physical processes
including the optical photon transport and coincidence conditions. The
agreement between the data and simulation (see counts per second versus
distances curves for three different radiation sources in Figure 13) validates
our Monte Carlo approach and physical parameters set. From these studies the
conversion curves are obtained by which the dose can be evaluated. In the end,
a final simulation is implemented to study the response of the device when
exposed to sources of ${}^{90}Sr$, ${}^{60}Co$ and ${}^{137}Cs$. In this last
work, also experimental data are taken to do a comparison with the simulated
one. The results confirm the agreement between simulated and experimental data
within the error bars for both gamma rays and beta particles. Through this
work, it will be possible to evaluate the dose from the counts per second
using the conversion curves found.

In the end, in the new version of the PDOZ, also the response to neutrons must
be studied. Therefore, in the final prototype, whose design includes particle
discrimination, it will be possible to detect, discriminate and evaluate the
dose released by beta particles, gamma rays and neutrons.

## References

## References

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