# Multi-Step Consistency Models: Fast Generation with Theoretical Guarantees arXiv: https://arxiv.org/abs/2505.01049 ยท HTML: https://mlsanity.com/paper/2505.01049/ ## Key facts - Cited by 2 papers in the map (data through 14 Oct 2026). - Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. - Builds on 34 of its 39 references that are in the map. - First posted on arXiv 2 May 2025. ## Placed in - Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/) ## Builds on (most cited first, 30 of 34) - [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020) - [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020) - [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020) - [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015) - [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019) - [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021) - [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022) - [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023) - [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022) - [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022) - [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021) - [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022) - [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023) - [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022) - [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023) - [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019) - [Diffusion Self-Guidance for Controllable Image Generation](https://mlsanity.com/paper/2306.00986/) (2023) - [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023) - [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022) - [Convergence for score-based generative modeling with polynomial complexity](https://mlsanity.com/paper/2206.06227/) (2022) - [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023) - [The probability flow ODE is provably fast](https://mlsanity.com/paper/2305.11798/) (2023) - [Fast ODE-based Sampling for Diffusion Models in Around 5 Steps](https://mlsanity.com/paper/2312.00094/) (2023) - [Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction](https://mlsanity.com/paper/2403.17042/) (2024) - [Multistep Consistency Models](https://mlsanity.com/paper/2403.06807/) (2024) - [A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models](https://mlsanity.com/paper/2408.02320/) (2024) - [Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistent](https://mlsanity.com/paper/2302.09057/) (2023) - [Convergence Analysis of Probability Flow ODE for Score-based Generative Models](https://mlsanity.com/paper/2404.09730/) (2024) - [Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distances](https://mlsanity.com/paper/2401.17958/) (2024) - [Efficient Diffusion Models for Vision: A Survey](https://mlsanity.com/paper/2210.09292/) (2022) ## Built on by (most cited first, 2 of 2) - [A Sharp KL-Convergence Analysis for Diffusion Models under Minimal Assumptions](https://mlsanity.com/paper/2508.16306/) (2025) - [Consistency Deep Equilibrium Models](https://mlsanity.com/paper/2602.03024/) (2026) ## Abstract (arXiv) 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(varepsilon2) using only Oleft(logleft(fracdvarepsilonright)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 Oleft(d logleft(fracdvarepsilonright)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.