Elucidating Flow Matching ODE Dynamics with Respect to Data Geometries

• URL: http://arxiv.org/abs/2412.18730v2
• Date: Fri, 10 Jan 2025 22:29:26 GMT
• Title: Elucidating Flow Matching ODE Dynamics with Respect to Data Geometries
• Authors: Zhengchao Wan, Qingsong Wang, Gal Mishne, Yusu Wang,
• Abstract summary: Diffusion-based generative models have become the standard for image generation. ODE-based samplers and flow matching models improve efficiency, in comparison to diffusion models, by reducing sampling steps through learned vector fields. We advance the theory of flow matching models through a comprehensive analysis of sample trajectories, centered on the denoiser that drives ODE dynamics. Our analysis reveals how trajectories evolve from capturing global data features to local structures, providing the geometric characterization of per-sample behavior in flow matching models.
• Score: 10.947094609205765
• License:
• Abstract: Diffusion-based generative models have become the standard for image generation. ODE-based samplers and flow matching models improve efficiency, in comparison to diffusion models, by reducing sampling steps through learned vector fields. However, the theoretical foundations of flow matching models remain limited, particularly regarding the convergence of individual sample trajectories at terminal time - a critical property that impacts sample quality and being critical assumption for models like the consistency model. In this paper, we advance the theory of flow matching models through a comprehensive analysis of sample trajectories, centered on the denoiser that drives ODE dynamics. We establish the existence, uniqueness and convergence of ODE trajectories at terminal time, ensuring stable sampling outcomes under minimal assumptions. Our analysis reveals how trajectories evolve from capturing global data features to local structures, providing the geometric characterization of per-sample behavior in flow matching models. We also explain the memorization phenomenon in diffusion-based training through our terminal time analysis. These findings bridge critical gaps in understanding flow matching models, with practical implications for sampling stability and model design.

Related papers

• Accelerated Diffusion Models via Speculative Sampling [89.43940130493233]
  Speculative sampling is a popular technique for accelerating inference in Large Language Models. We extend speculative sampling to diffusion models, which generate samples via continuous, vector-valued Markov chains. We propose various drafting strategies, including a simple and effective approach that does not require training a draft model.
  arXiv  Detail & Related papers  (2025-01-09T16:50:16Z)
• A precise asymptotic analysis of learning diffusion models: theory and insights [37.30894159200853]
  We consider the problem of learning a flow or diffusion-based generative model parametrized by a two-layer auto-encoder. We derive a tight characterization of low-dimensional projections of the distribution of samples generated by the learned model.
  arXiv  Detail & Related papers  (2025-01-07T16:56:40Z)
• Provable Statistical Rates for Consistency Diffusion Models [87.28777947976573]
  Despite the state-of-the-art performance, diffusion models are known for their slow sample generation due to the extensive number of steps involved. This paper contributes towards the first statistical theory for consistency models, formulating their training as a distribution discrepancy minimization problem.
  arXiv  Detail & Related papers  (2024-06-23T20:34:18Z)
• Latent diffusion models for parameterization and data assimilation of facies-based geomodels [0.0]
  Diffusion models are trained to generate new geological realizations from input fields characterized by random noise. Latent diffusion models are shown to provide realizations that are visually consistent with samples from geomodeling software.
  arXiv  Detail & Related papers  (2024-06-21T01:32:03Z)
• On the Trajectory Regularity of ODE-based Diffusion Sampling [79.17334230868693]
  Diffusion-based generative models use differential equations to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models.
  arXiv  Detail & Related papers  (2024-05-18T15:59:41Z)
• Towards Theoretical Understandings of Self-Consuming Generative Models [56.84592466204185]
  This paper tackles the emerging challenge of training generative models within a self-consuming loop. We construct a theoretical framework to rigorously evaluate how this training procedure impacts the data distributions learned by future models. We present results for kernel density estimation, delivering nuanced insights such as the impact of mixed data training on error propagation.
  arXiv  Detail & Related papers  (2024-02-19T02:08:09Z)
• A Geometric Perspective on Diffusion Models [57.27857591493788]
  We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
  arXiv  Detail & Related papers  (2023-05-31T15:33:16Z)
• Reflected Diffusion Models [93.26107023470979]
  We present Reflected Diffusion Models, which reverse a reflected differential equation evolving on the support of the data. Our approach learns the score function through a generalized score matching loss and extends key components of standard diffusion models.
  arXiv  Detail & Related papers  (2023-04-10T17:54:38Z)

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.