# A Sharp KL-Convergence Analysis for Diffusion Models under Minimal Assumptions arXiv: https://arxiv.org/abs/2508.16306 · HTML: https://mlsanity.com/paper/2508.16306/ ## Key facts - Cited by 8 papers in the map (data through 14 Oct 2026). - Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. - Builds on 28 of its 31 references that are in the map. - First posted on arXiv 22 Aug 2025. ## Placed in - Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/) ## Builds on (most cited first, 28 of 28) - [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) - [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) - [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023) - [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022) - [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (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) - [AudioLDM: Text-to-Audio Generation with Latent Diffusion Models](https://mlsanity.com/paper/2301.12503/) (2023) - [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022) - [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) - [Improved analysis for a proximal algorithm for sampling](https://mlsanity.com/paper/2202.06386/) (2022) - [Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction](https://mlsanity.com/paper/2403.17042/) (2024) - [A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models](https://mlsanity.com/paper/2408.02320/) (2024) - [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) - [O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions](https://mlsanity.com/paper/2409.18959/) (2024) - [Towards a mathematical theory for consistency training in diffusion models](https://mlsanity.com/paper/2402.07802/) (2024) - [Unified Convergence Analysis for Score-Based Diffusion Models with Deterministic Samplers](https://mlsanity.com/paper/2410.14237/) (2024) - [Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimation](https://mlsanity.com/paper/2303.03237/) (2023) - [Multi-Step Consistency Models: Fast Generation with Theoretical Guarantees](https://mlsanity.com/paper/2505.01049/) (2025) ## Built on by (most cited first, 8 of 8) - [Optimal Convergence Analysis of DDPM for General Distributions](https://mlsanity.com/paper/2510.27562/) (2025) - [High-accuracy sampling for diffusion models and log-concave distributions](https://mlsanity.com/paper/2602.01338/) (2026) - [Wasserstein bounds for denoising diffusion probabilistic models via the F"ollmer process](https://mlsanity.com/paper/2605.18069/) (2026) - [ConvergeFlow: Language Flow with Provable Convergence to Token Embeddings](https://mlsanity.com/paper/2608.23551/) (2026) - [Connections between the F"ollmer process and the denoising diffusion probabilistic model](https://mlsanity.com/paper/2605.18040/) (2026) - [The Value of Covariance Matching in Gaussian DDPMs and the Lanczos Sampler](https://mlsanity.com/paper/2605.22723/) (2026) - [Semi-Supervised Conditional Generative Learning through Stochastic Interpolation and Sufficient Representations](https://mlsanity.com/paper/2607.16725/) (2026) - [Sharp Convergence and Sampling Trade-offs for Riemannian Diffusion under Nonnegative Ricci Curvature](https://mlsanity.com/paper/2609.36568/) (2026) ## Abstract (arXiv) Diffusion-based generative models have emerged as highly effective methods for synthesizing high-quality samples. Recent works have focused on analyzing the convergence of their generation process with minimal assumptions, either through reverse SDEs or Probability Flow ODEs. The best known guarantees, without any smoothness assumptions, for the KL divergence so far achieve a linear dependence on the data dimension d and an inverse quadratic dependence on varepsilon. In this work, we present a refined analysis that improves the dependence on varepsilon. We model the generation process as a composition of two steps: a reverse ODE step, followed by a smaller noising step along the forward process. This design leverages the fact that the ODE step enables control in Wasserstein-type error, which can then be converted into a KL divergence bound via noise addition, leading to a better dependence on the discretization step size. We further provide a novel analysis to achieve the linear d-dependence for the error due to discretizing this Probability Flow ODE in absence of any smoothness assumptions. We show that tildeOleft(tfracdlog3/2(frac1δ)varepsilonright) steps suffice to approximate the target distribution corrupted with Gaussian noise of variance δ within O(varepsilon2) in KL divergence, improving upon the previous best result, requiring tildeOleft(tfracdlog2(frac1δ)varepsilon2right) steps.