Towards a mathematical theory for consistency training in diffusion models

• URL: http://arxiv.org/abs/2402.07802v1
• Date: Mon, 12 Feb 2024 17:07:02 GMT
• Title: Towards a mathematical theory for consistency training in diffusion models
• Authors: Gen Li, Zhihan Huang, Yuting Wei
• Abstract summary: This paper takes a first step towards establishing theoretical underpinnings for consistency models. We demonstrate that, in order to generate samples within $varepsilon$ proximity to the target in distribution, it suffices for the number of steps in consistency learning to exceed the order of $d5/2/varepsilon$, with the data dimension. Our theory offers rigorous insights into the validity and efficacy of consistency models, illuminating their utility in downstream inference tasks.
• Score: 17.632123036281957
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Consistency models, which were proposed to mitigate the high computational overhead during the sampling phase of diffusion models, facilitate single-step sampling while attaining state-of-the-art empirical performance. When integrated into the training phase, consistency models attempt to train a sequence of consistency functions capable of mapping any point at any time step of the diffusion process to its starting point. Despite the empirical success, a comprehensive theoretical understanding of consistency training remains elusive. This paper takes a first step towards establishing theoretical underpinnings for consistency models. We demonstrate that, in order to generate samples within $\varepsilon$ proximity to the target in distribution (measured by some Wasserstein metric), it suffices for the number of steps in consistency learning to exceed the order of $d^{5/2}/\varepsilon$, with $d$ the data dimension. Our theory offers rigorous insights into the validity and efficacy of consistency models, illuminating their utility in downstream inference tasks.

Related papers

• Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
  We present the first performance guarantee with explicit dimensional general score-mismatched diffusion samplers. We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions. This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
  arXiv  Detail & Related papers  (2024-10-17T16:42:12Z)
• Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis [56.442307356162864]
  We study the theoretical aspects of score-based discrete diffusion models under the Continuous Time Markov Chain (CTMC) framework. We introduce a discrete-time sampling algorithm in the general state space $[S]d$ that utilizes score estimators at predefined time points. Our convergence analysis employs a Girsanov-based method and establishes key properties of the discrete score function.
  arXiv  Detail & Related papers  (2024-10-03T09:07:13Z)
• A Score-Based Density Formula, with Applications in Diffusion Generative Models [6.76974373198208]
  Score-based generative models (SGMs) have revolutionized the field of generative modeling, achieving unprecedented success in generating realistic and diverse content. Despite empirical advances, the theoretical basis for why optimizing the evidence lower bound (ELBO) on the log-likelihood is effective for training diffusion generative models, such as DDPMs, remains largely unexplored.
  arXiv  Detail & Related papers  (2024-08-29T17:59:07Z)
• 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)
• Improving Consistency Models with Generator-Induced Flows [16.049476783301724]
  Consistency models imitate the multi-step sampling of score-based diffusion in a single forward pass of a neural network. They can be learned in two ways: consistency distillation and consistency training. We propose a novel flow that transports noisy data towards their corresponding outputs derived from the currently trained model.
  arXiv  Detail & Related papers  (2024-06-13T20:22:38Z)
• Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory [87.00653989457834]
  Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. Despite the empirical success, theory of conditional diffusion models is largely missing. This paper bridges the gap by presenting a sharp statistical theory of distribution estimation using conditional diffusion models.
  arXiv  Detail & Related papers  (2024-03-18T17:08:24Z)
• 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)
• Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformization [17.535229185525353]
  We introduce an algorithm leveraging the uniformization of continuous Markov chains, implementing transitions on random time points. Our results align with state-of-the-art achievements for diffusion models in $mathbbRd$ and further underscore the advantages of discrete diffusion models in comparison to the $mathbbRd$ setting.
  arXiv  Detail & Related papers  (2024-02-12T22:26:52Z)
• How Much is Enough? A Study on Diffusion Times in Score-based Generative Models [76.76860707897413]
  Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution. We show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process.
  arXiv  Detail & Related papers  (2022-06-10T15:09:46Z)

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.