mlsanityData to 7 Oct 2026

High-accuracy sampling for diffusion models and log-concave distributions

arXiv 2602.01338 ↗First posted 1 Feb 2026cs.LG math.ST stat.MLcited by 13

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We present algorithms for diffusion model sampling which obtain δ-error in polylog(1/δ) steps, given access to widetilde O(δ)-accurate score estimates in L2. This is an exponential improvement over all previous results. Specifically, under minimal data assumptions, the complexity is widetilde O(d_star polylog(1/δ)) where d_star is the intrinsic dimension of the data. Further, under a non-uniform L-Lipschitz condition, the complexity reduces to widetilde O(L polylog(1/δ)). Our approach also yields the first polylog(1/δ) complexity sampler for general log-concave distributions using only gradient evaluations.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 36 of its 48 references that are in the map. First posted on arXiv 1 Feb 2026.

Builds on

36 of 48 references.

Closest ancestors · 29

Same direction, newest first

  1. 2026High-accuracy and dimension-free sampling with diffusions15 Jan
  2. 2025Sublinear iterations can suffice even for DDPMs6 Nov
  3. 2025Optimal Convergence Analysis of DDPM for General Distributions31 Oct
  4. 2025A Sharp KL-Convergence Analysis for Diffusion Models under Minimal Assumptions22 Aug
  5. 2025Faster Diffusion Models via Higher-Order Approximation30 Jun
  6. 2025Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models16 Jun
  7. 2025Almost Linear Convergence under Minimal Score Assumptions: Quantized Transition Diffusion28 May
  8. 2025Dimension-Free Convergence of Diffusion Models for Approximate Gaussian Mixtures7 Apr
  9. 2025Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models31 Jan
  10. 2025Low-dimensional adaptation of diffusion models: Convergence in total variation22 Jan
  11. 2024Provable Acceleration for Diffusion Models under Minimal Assumptions30 Oct
  12. 2024Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality24 Oct
17 more
  1. 2024Instance-dependent Convergence Theory for Diffusion Models17 Oct
  2. 2024Linear Convergence of Diffusion Models Under the Manifold Hypothesis11 Oct
  3. 2024Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions27 Sep
  4. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models5 Aug
  5. 2024Reverse Transition Kernel: A Flexible Framework to Accelerate Diffusion Inference26 May
  6. 2024Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models23 May
  7. 2024Convergence Analysis of Probability Flow ODE for Score-based Generative Models15 Apr
  8. 2024Accelerating Convergence of Score-Based Diffusion Models, Provably6 Mar
  9. 2024Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distances31 Jan
  10. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models18 Nov
  11. 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptions23 Aug
  12. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  13. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models15 Jun
  14. 2023The probability flow ODE is provably fast19 May
  15. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  16. 2022Convergence of score-based generative modeling for general data distributions26 Sep
  17. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep

Other references · 7

  1. 2020Structured Logconcave Sampling with a Restricted Gaussian Oraclecited by 85
  2. 2022Improved analysis for a proximal algorithm for samplingcited by 72
  3. 2023Faster high-accuracy log-concave sampling via algorithmic warm startscited by 44
  4. 2023Improved dimension dependence of a proximal algorithm for samplingcited by 29
  5. 2024Online Estimation via Offline Estimation: An Information-Theoretic Frameworkcited by 11
  6. 2020Complexity of zigzag sampling algorithm for strongly log-concave distributionscited by 5
  7. 2025Fast Score-Based Sampling via Log-Concave Reductionscited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 13.

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  1. 2026Blind denoising diffusion models and the blessings of dimensionalitycited by 8
  2. 2026High-accuracy log-concave sampling with stochastic queriescited by 2
  3. 2026Query Lower Bounds for Diffusion Samplingcited by 2
  4. 2026Denoising growth complexity: Data geometry and certified schedules for diffusion samplingcited by 2
  5. 2026Load--Reserve Wasserstein Propagation for Isotropic Diffusion Samplerscited by 1
  6. 2026Metropolis-Adjusted Diffusion Modelscited by 1
  7. 2026A proximal gradient algorithm for composite log-concave samplingcited by 1
  8. 2026A Mathematical Introduction to Diffusion Modelscited by 1
  9. 2026Windowed thinning and query complexity for the bouncy particle and Zigzag samplerscited by 1
  10. 2026Complexity of Non-Log-Concave Sampling in Fisher Informationcited by 0
  11. 2026Smoothed Score Queries and the Complexity of Samplingcited by 0
  12. 2026Accelerated High-Accuracy Sampling from a Warm Start via the Proximal Bouncy Particle Samplercited by 0
1 more
  1. 2026Local Geometric Mixing via Dobrushin Contraction with Applications to Diffusion Path Monte Carlo and the Proximal Samplercited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallel
  2. 2024Parallel Simulation for Log-concave Sampling and Score-based Diffusion Models
  3. 2026Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees
  4. 2023On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates
  5. 2026Wasserstein bounds for denoising diffusion probabilistic models via the F"ollmer process
  6. 2026Diffusion Models Are Statistically Optimal for Learning Low-Dimensional Multi-Modal Distributions
  7. 2025Minimax Optimality of the Probability Flow ODE for Diffusion Models
  8. 2023Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers