Latent Abstractions in Generative Diffusion Models
- URL: http://arxiv.org/abs/2410.03368v1
- Date: Fri, 4 Oct 2024 12:34:24 GMT
- Title: Latent Abstractions in Generative Diffusion Models
- Authors: Giulio Franzese, Mattia Martini, Giulio Corallo, Paolo Papotti, Pietro Michiardi,
- Abstract summary: We study how diffusion-based generative models produce high-dimensional data, such as an image, by implicitly relying on a manifestation of a low-dimensional set of latent abstractions.
We present a novel theoretical framework that extends NLF, and that offers a unique perspective on SDE-based generative models.
- Score: 13.344019183402867
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In this work we study how diffusion-based generative models produce high-dimensional data, such as an image, by implicitly relying on a manifestation of a low-dimensional set of latent abstractions, that guide the generative process. We present a novel theoretical framework that extends NLF, and that offers a unique perspective on SDE-based generative models. The development of our theory relies on a novel formulation of the joint (state and measurement) dynamics, and an information-theoretic measure of the influence of the system state on the measurement process. According to our theory, diffusion models can be cast as a system of SDE, describing a non-linear filter in which the evolution of unobservable latent abstractions steers the dynamics of an observable measurement process (corresponding to the generative pathways). In addition, we present an empirical study to validate our theory and previous empirical results on the emergence of latent abstractions at different stages of the generative process.
Related papers
- Can Diffusion Models Disentangle? A Theoretical Perspective [52.360881354319986]
This paper presents a novel theoretical framework for understanding how diffusion models can learn disentangled representations.
We establish identifiability conditions for general disentangled latent variable models, analyze training dynamics, and derive sample complexity bounds for disentangled latent subspace models.
arXiv Detail & Related papers (2025-03-31T20:46:18Z) - Geometric Trajectory Diffusion Models [58.853975433383326]
Generative models have shown great promise in generating 3D geometric systems.
Existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature.
We propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories.
arXiv Detail & Related papers (2024-10-16T20:36:41Z) - Neural Message Passing Induced by Energy-Constrained Diffusion [79.9193447649011]
We propose an energy-constrained diffusion model as a principled interpretable framework for understanding the mechanism of MPNNs.
We show that the new model can yield promising performance for cases where the data structures are observed (as a graph), partially observed or completely unobserved.
arXiv Detail & Related papers (2024-09-13T17:54:41Z) - Learning Discrete Concepts in Latent Hierarchical Models [73.01229236386148]
Learning concepts from natural high-dimensional data holds potential in building human-aligned and interpretable machine learning models.
We formalize concepts as discrete latent causal variables that are related via a hierarchical causal model.
We substantiate our theoretical claims with synthetic data experiments.
arXiv Detail & Related papers (2024-06-01T18:01:03Z) - Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling [2.1779479916071067]
We introduce a novel framework that enhances diffusion models by supporting a broader range of forward processes.
We also propose a novel parameterization technique for learning the forward process.
Results underscore NFDM's versatility and its potential for a wide range of applications.
arXiv Detail & Related papers (2024-04-19T15:10:54Z) - An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization [59.63880337156392]
Diffusion models have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology.
Despite the significant empirical success, theory of diffusion models is very limited.
This paper provides a well-rounded theoretical exposure for stimulating forward-looking theories and methods of diffusion models.
arXiv Detail & Related papers (2024-04-11T14:07:25Z) - ODE-based Recurrent Model-free Reinforcement Learning for POMDPs [15.030970899252601]
We present a novel ODE-based recurrent model combines with model-free reinforcement learning framework to solve POMDPs.
We experimentally demonstrate the efficacy of our methods across various PO continuous control and meta-RL tasks.
Our experiments illustrate that our method is robust against irregular observations, owing to the ability of ODEs to model irregularly-sampled time series.
arXiv Detail & Related papers (2023-09-25T12:13:56Z) - Geometric Neural Diffusion Processes [55.891428654434634]
We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling.
We show that with these conditions, the generative functional model admits the same symmetry.
arXiv Detail & Related papers (2023-07-11T16:51:38Z) - Interpretable ODE-style Generative Diffusion Model via Force Field
Construction [0.0]
This paper aims to identify various physical models that are suitable for constructing ODE-style generative diffusion models accurately from a mathematical perspective.
We perform a case study where we use the theoretical model identified by our method to develop a range of new diffusion model methods.
arXiv Detail & Related papers (2023-03-14T16:58:11Z) - A Reparameterized Discrete Diffusion Model for Text Generation [39.0145272152805]
This work studies discrete diffusion probabilistic models with applications to natural language generation.
We derive an alternative yet equivalent formulation of the sampling from discrete diffusion processes.
We conduct extensive experiments to evaluate the text generation capability of our model, demonstrating significant improvements over existing diffusion models.
arXiv Detail & Related papers (2023-02-11T16:26:57Z) - An optimal control perspective on diffusion-based generative modeling [9.806130366152194]
We establish a connection between optimal control and generative models based on differential equations (SDEs)
In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals.
We develop a novel diffusion-based method for sampling from unnormalized densities.
arXiv Detail & Related papers (2022-11-02T17:59:09Z) - A Survey on Generative Diffusion Model [75.93774014861978]
Diffusion models are an emerging class of deep generative models.
They have certain limitations, including a time-consuming iterative generation process and confinement to high-dimensional Euclidean space.
This survey presents a plethora of advanced techniques aimed at enhancing diffusion models.
arXiv Detail & Related papers (2022-09-06T16:56:21Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.