# High-accuracy and dimension-free sampling with diffusions arXiv: https://arxiv.org/abs/2601.10708 ยท HTML: https://mlsanity.com/paper/2601.10708/ ## Key facts - Cited by 7 papers in the map (data through 7 Oct 2026). - Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. - Builds on 57 of its 65 references that are in the map. - First posted on arXiv 15 Jan 2026. ## Placed in - Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/) ## Builds on (most cited first, 30 of 57) - [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020) - [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020) - [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021) - [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) - [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022) - [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022) - [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021) - [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021) - [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021) - [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023) - [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022) - [Convergence of denoising diffusion models under the manifold hypothesis](https://mlsanity.com/paper/2208.05314/) (2022) - [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 of score-based generative modeling for general data distributions](https://mlsanity.com/paper/2209.12381/) (2022) - [Convergence for score-based generative modeling with polynomial complexity](https://mlsanity.com/paper/2206.06227/) (2022) - [The probability flow ODE is provably fast](https://mlsanity.com/paper/2305.11798/) (2023) - [Score-Based Generative Models Detect Manifolds](https://mlsanity.com/paper/2206.01018/) (2022) - [Generative Modeling with Denoising Auto-Encoders and Langevin Sampling](https://mlsanity.com/paper/2002.00107/) (2020) - [Log-concave sampling: Metropolis-Hastings algorithms are fast](https://mlsanity.com/paper/1801.02309/) (2018) - [Parallel Sampling of Diffusion Models](https://mlsanity.com/paper/2305.16317/) (2023) - [Let us Build Bridges: Understanding and Extending Diffusion Generative Models](https://mlsanity.com/paper/2208.14699/) (2022) - [Error Bounds for Flow Matching Methods](https://mlsanity.com/paper/2305.16860/) (2023) - [Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models](https://mlsanity.com/paper/2306.09251/) (2023) - [Mixture Models, Robustness, and Sum of Squares Proofs](https://mlsanity.com/paper/1711.07454/) (2017) - [Accelerating Convergence of Score-Based Diffusion Models, Provably](https://mlsanity.com/paper/2403.03852/) (2024) - [Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers](https://mlsanity.com/paper/2303.03384/) (2023) - [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024) - [List-Decodable Robust Mean Estimation and Learning Mixtures of Spherical Gaussians](https://mlsanity.com/paper/1711.07211/) (2017) ## Built on by (most cited first, 7 of 7) - [Confidence-Based Decoding is Provably Efficient for Diffusion Language Models](https://mlsanity.com/paper/2603.22248/) (2026) - [High-accuracy sampling for diffusion models and log-concave distributions](https://mlsanity.com/paper/2602.01338/) (2026) - [Adaptation to Intrinsic Dependence in Diffusion Language Models](https://mlsanity.com/paper/2602.20126/) (2026) - [Blind denoising diffusion models and the blessings of dimensionality](https://mlsanity.com/paper/2602.09639/) (2026) - [Query Lower Bounds for Diffusion Sampling](https://mlsanity.com/paper/2604.10857/) (2026) - [Denoising growth complexity: Data geometry and certified schedules for diffusion sampling](https://mlsanity.com/paper/2607.26285/) (2026) - [Entropy-Based Dimension-Free Convergence and Loss-Adaptive Schedules for Diffusion Models](https://mlsanity.com/paper/2601.21943/) (2026) ## Abstract (arXiv) Diffusion models have shown remarkable empirical success in sampling from rich multi-modal distributions. Their inference relies on numerically solving a certain differential equation. This differential equation cannot be solved in closed form, and its resolution via discretization typically requires many small iterations to produce high-quality samples. More precisely, prior works have shown that the iteration complexity of discretization methods for diffusion models scales polynomially in the ambient dimension and the inverse accuracy 1/varepsilon. In this work, we propose a new solver for diffusion models relying on a subtle interplay between low-degree approximation and the collocation method (Lee, Song, Vempala 2018), and we prove that its iteration complexity scales polylogarithmically in 1/varepsilon, yielding the first ``high-accuracy'' guarantee for a diffusion-based sampler that only uses (approximate) access to the scores of the data distribution. In addition, our bound does not depend explicitly on the ambient dimension; more precisely, the dimension affects the complexity of our solver through the effective radius of the support of the target distribution only.