mlsanityData to 7 Oct 2026

Parallel Simulation for Log-concave Sampling and Score-based Diffusion Models

arXiv 2412.07435 ↗First posted 10 Dec 2024cs.DS cs.DC cs.LGcited by 6

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Sampling from high-dimensional probability distributions is fundamental in machine learning and statistics. As datasets grow larger, computational efficiency becomes increasingly important, particularly in reducing adaptive complexity, namely the number of sequential rounds required for sampling algorithms. While recent works have introduced several parallelizable techniques, they often exhibit suboptimal convergence rates and remain significantly weaker than the latest lower bounds for log-concave sampling. To address this, we propose a novel parallel sampling method that improves adaptive complexity dependence on dimension d reducing it from widetildeO(log2 d) to widetildeO(log d). which is even optimal for log-concave sampling with some specific adaptive complexity. Our approach builds on parallel simulation techniques from scientific computing.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 45 of its 70 references that are in the map. First posted on arXiv 10 Dec 2024.

Builds on

45 of 70 references.

Closest ancestors · 24

Same direction, newest first

  1. 2024SwiftDiffusion: Efficient Diffusion Model Serving with Add-on Modules2 Jul
  2. 2024Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallel3 Jun
  3. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity24 May
  4. 2024Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models23 May
  5. 2024Convergence Analysis of Probability Flow ODE for Score-based Generative Models15 Apr
  6. 2024DistriFusion: Distributed Parallel Inference for High-Resolution Diffusion Models29 Feb
  7. 2024Broadening Target Distributions for Accelerated Diffusion Models via a Novel Analysis Approach21 Feb
  8. 2024Contractive Diffusion Probabilistic Models23 Jan
  9. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  10. 2023Lipschitz Singularities in Diffusion Models20 Jun
  11. 2023Parallel Sampling of Diffusion Models25 May
  12. 2023Improved Convergence of Score-Based Diffusion Models via Prediction-Correction23 May
12 more
  1. 2023The probability flow ODE is provably fast19 May
  2. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  3. 2022DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models2 Nov
  4. 2022Convergence of score-based generative modeling for general data distributions26 Sep
  5. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  6. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  7. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  8. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  9. 2021Cascaded Diffusion Models for High Fidelity Image Generation30 May
  10. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  11. 2020Denoising Diffusion Implicit Models6 Oct
  12. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 21

  1. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  2. 2022Video Diffusion Modelscited by 2,280
  3. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  4. 2022Diffusion Probabilistic Modeling for Video Generationcited by 237
  5. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  6. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  7. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 195
  8. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  9. 2018Log-concave sampling: Metropolis-Hastings algorithms are fastcited by 117
  10. 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 77
  11. 2022Can Push-forward Generative Models Fit Multimodal Distributions?cited by 41
  12. 2019High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithmcited by 36
9 more
  1. 2019Stochastic Runge-Kutta Accelerates Langevin Monte Carlo and Beyondcited by 33
  2. 2019Proximal Langevin Algorithm: Rapid Convergence Under Isoperimetrycited by 31
  3. 2022Resolving the Mixing Time of the Langevin Algorithm to its Stationary Distribution for Log-Concave Samplingcited by 21
  4. 2024Fast parallel sampling under isoperimetrycited by 12
  5. 2022Parallel MCMC Without Embarrassing Failurescited by 11
  6. 2024Parallelized Midpoint Randomization for Langevin Monte Carlocited by 9
  7. 2023Streaming Euclidean k-median and k-means with o(log n) Spacecited by 7
  8. 2024Kinetic Interacting Particle Langevin Monte Carlocited by 7
  9. 2019Implicit Langevin Algorithms for Sampling From Log-concave Densitiescited by 6

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 3.

6 papers.

  1. 2025Accelerated Diffusion Models via Speculative Samplingcited by 30
  2. 2025Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyondcited by 11
  3. 2025Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Modelscited by 9
  4. 2026Accelerating Diffusion Sampling via Speculative Draft Treescited by 2
  5. 2026Accelerating Discrete Diffusion Models with Parallel-In-Time Samplingcited by 1
  6. 2026Rank-Aware Speculative Sampling for Diffusion Draft Treescited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026High-accuracy sampling for diffusion models and log-concave distributions
  2. 2026Lower Bounds for Parallel Diffusion Sampling
  3. 2026Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees
  4. 2026Provably adaptive sampling with uniform and remasking discrete diffusion models
  5. 2026Query Lower Bounds for Diffusion Sampling
  6. 2026Denoising growth complexity: Data geometry and certified schedules for diffusion sampling
  7. 2025Parallel Sampling via Autospeculation
  8. 2025Sublinear iterations can suffice even for DDPMs