Multi-Step Consistency Models: Fast Generation with Theoretical Guarantees

• URL: http://arxiv.org/abs/2505.01049v2
• Date: Sun, 25 May 2025 04:06:45 GMT
• Title: Multi-Step Consistency Models: Fast Generation with Theoretical Guarantees
• Authors: Nishant Jain, Xunpeng Huang, Yian Ma, Tong Zhang,
• Abstract summary: We provide a theoretical analysis of consistency models capable of mapping inputs at a given time to arbitrary points along the reverse trajectory.<n>We show that one can achieve a KL divergence of order $ O(varepsilon2) $ using only $ Oleft(logleft(fracdvarepsilonright) $ iterations with a constant step size.<n>We conclude that accurate learning is feasible using small discretization steps, both in smooth and non-smooth settings.
• Score: 15.366598179769918
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Consistency models have recently emerged as a compelling alternative to traditional SDE-based diffusion models. They offer a significant acceleration in generation by producing high-quality samples in very few steps. Despite their empirical success, a proper theoretic justification for their speed-up is still lacking. In this work, we address the gap by providing a theoretical analysis of consistency models capable of mapping inputs at a given time to arbitrary points along the reverse trajectory. We show that one can achieve a KL divergence of order $ O(\varepsilon^2) $ using only $ O\left(\log\left(\frac{d}{\varepsilon}\right)\right) $ iterations with a constant step size. Additionally, under minimal assumptions on the data distribution (non smooth case) an increasingly common setting in recent diffusion model analyses we show that a similar KL convergence guarantee can be obtained, with the number of steps scaling as $ O\left(d \log\left(\frac{d}{\varepsilon}\right)\right) $. Going further, we also provide a theoretical analysis for estimation of such consistency models, concluding that accurate learning is feasible using small discretization steps, both in smooth and non-smooth settings. Notably, our results for the non-smooth case yield best in class convergence rates compared to existing SDE or ODE based analyses under minimal assumptions.

Related papers

• Beyond Scores: Proximal Diffusion Models [10.27283386401996]
  We develop Proximal Diffusion Models (ProxDM) to learn proximal operators of the log-density.<n>We show that two variants of ProxDM achieve significantly faster within just a few sampling steps compared to conventional score-matching methods.
  arXiv  Detail & Related papers  (2025-07-11T18:30:09Z)
• Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Acceleration [5.548787731232499]
  We focus on the Wasserstein convergence analysis of score-based diffusion models.<n>We compare various discretization schemes, including Euler discretization, exponential midpoint and randomization methods.<n>We propose an accelerated sampler based on the local linearization method.
  arXiv  Detail & Related papers  (2025-02-07T11:37:51Z)
• Improved Convergence Rate for Diffusion Probabilistic Models [7.237817437521988]
  Score-based diffusion models have achieved remarkable empirical performance in the field of machine learning and artificial intelligence. Despite a lot of theoretical attempts, there still exists significant gap between theory and practice. We establish an iteration complexity at the order of $d2/3varepsilon-2/3$, which is better than $d5/12varepsilon-1$. Our theory accommodates $varepsilon$-accurate score estimates, and does not require log-concavity on the target distribution.
  arXiv  Detail & Related papers  (2024-10-17T16:37:33Z)
• 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.<n>We introduce a discrete-time sampling algorithm in the general state space $[S]d$ that utilizes score estimators at predefined time points.<n>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)
• O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions [6.76974373198208]
  We establish a fast convergence theory for the denoising diffusion probabilistic model (DDPM) under minimal assumptions.<n>We show that the convergence rate improves to $O(k/T)$, where $k$ is the intrinsic dimension of the target data distribution.<n>This highlights the ability of DDPM to automatically adapt to unknown low-dimensional structures.
  arXiv  Detail & Related papers  (2024-09-27T17:59:10Z)
• A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models [45.60426164657739]
  We develop non-asymptotic convergence theory for a diffusion-based sampler. We prove that $d/varepsilon$ are sufficient to approximate the target distribution to within $varepsilon$ total-variation distance. Our results also characterize how $ell$ score estimation errors affect the quality of the data generation processes.
  arXiv  Detail & Related papers  (2024-08-05T09:02:24Z)
• Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity [11.71206628091551]
  Diffusion models are costly to train and evaluate, reducing the inference cost for diffusion models remains a major goal. Inspired by the recent empirical success in accelerating diffusion models via the parallel sampling techniqueciteshih2024parallel, we propose to divide the sampling process into $mathcalO(1)$ blocks with parallelizable Picard iterations within each block. Our results shed light on the potential of fast and efficient sampling of high-dimensional data on fast-evolving modern large-memory GPU clusters.
  arXiv  Detail & Related papers  (2024-05-24T23:59:41Z)
• Broadening Target Distributions for Accelerated Diffusion Models via a Novel Analysis Approach [49.97755400231656]
  We show that a new accelerated DDPM sampler achieves accelerated performance for three broad distribution classes not considered before.<n>Our results show an improved dependency on the data dimension $d$ among accelerated DDPM type samplers.
  arXiv  Detail & Related papers  (2024-02-21T16:11:47Z)
• Gaussian Mixture Solvers for Diffusion Models [84.83349474361204]
  We introduce a novel class of SDE-based solvers called GMS for diffusion models. Our solver outperforms numerous SDE-based solvers in terms of sample quality in image generation and stroke-based synthesis.
  arXiv  Detail & Related papers  (2023-11-02T02:05:38Z)
• Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models [49.81937966106691]
  We develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach.
  arXiv  Detail & Related papers  (2023-06-15T16:30:08Z)
• Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions [9.953088581242845]
  We provide convergence guarantees with complexity for any data distribution with second-order moment. Our result does not rely on any log-concavity or functional inequality assumption. Our theoretical analysis provides comparison between different discrete approximations and may guide the choice of discretization points in practice.
  arXiv  Detail & Related papers  (2022-11-03T15:51:00Z)
• Sharper Rates and Flexible Framework for Nonconvex SGD with Client and Data Sampling [64.31011847952006]
  We revisit the problem of finding an approximately stationary point of the average of $n$ smooth and possibly non-color functions. We generalize the $smallsfcolorgreen$ so that it can provably work with virtually any sampling mechanism. We provide the most general and most accurate analysis of optimal bound in the smooth non-color regime.
  arXiv  Detail & Related papers  (2022-06-05T21:32:33Z)
• KL-Entropy-Regularized RL with a Generative Model is Minimax Optimal [70.15267479220691]
  We consider and analyze the sample complexity of model reinforcement learning with a generative variance-free model. Our analysis shows that it is nearly minimax-optimal for finding an $varepsilon$-optimal policy when $varepsilon$ is sufficiently small.
  arXiv  Detail & Related papers  (2022-05-27T19:39:24Z)
• Faster Convergence of Stochastic Gradient Langevin Dynamics for Non-Log-Concave Sampling [110.88857917726276]
  We provide a new convergence analysis of gradient Langevin dynamics (SGLD) for sampling from a class of distributions that can be non-log-concave. At the core of our approach is a novel conductance analysis of SGLD using an auxiliary time-reversible Markov Chain.
  arXiv  Detail & Related papers  (2020-10-19T15:23:18Z)

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.