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

• URL: http://arxiv.org/abs/2412.07435v3
• Date: Mon, 22 Sep 2025 14:12:23 GMT
• Title: Parallel Simulation for Log-concave Sampling and Score-based Diffusion Models
• Authors: Huanjian Zhou, Masashi Sugiyama,
• Abstract summary: We propose a novel parallel sampling method that improves adaptive complexity dependence on dimension $d$.<n>Our approach builds on parallel simulation techniques from scientific computing.
• Score: 55.07411490538404
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $\widetilde{\mathcal{O}}(\log^2 d)$ to $\widetilde{\mathcal{O}}(\log d)$. which is even optimal for log-concave sampling with some specific adaptive complexity. Our approach builds on parallel simulation techniques from scientific computing.

Related papers

• Nested Slice Sampling: Vectorized Nested Sampling for GPU-Accelerated Inference [0.4999814847776097]
  This paper introduces Nested Slice Sampling (NSS), a GPU-friendly, vectorized formulation of Nested Sampling.<n>A tuning analysis yields a simple near-optimal rule for setting the slice width, improving high-dimensional behavior and making per-step compute more predictable.
  arXiv  Detail & Related papers  (2026-01-30T18:20:32Z)
• Fast Gibbs Sampling on Bayesian Hidden Markov Model with Missing Observations [0.30586855806896046]
  The Hidden Markov Model (MM) is a widely-used statistical model for handling sequential data.<n>missing observations in real-world datasets often show up in numerical simulations and real data.<n>We propose an algorithm that estimates both the number of missing entries and the time complexity of a lot.<n>The proposed algorithm produces a larger Effective Sample Size (ESS) per summary, which can be justified theoretically and theoretically.
  arXiv  Detail & Related papers  (2026-01-04T09:10:43Z)
• Mean-Field Simulation-Based Inference for Cosmological Initial Conditions [4.520518890664213]
  We present a simple method for Bayesian field reconstruction based on modeling the posterior distribution of the initial matter density field to be diagonal Gaussian in Fourier space. Training and sampling are extremely fast (training: $sim 1, mathrmh$ on a GPU, sampling: $lesssim 3, mathrms$ for 1000 samples at resolution $1283$), and our method supports industry-standard (non-differentiable) $N$-body simulators.
  arXiv  Detail & Related papers  (2024-10-21T09:23:50Z)
• Bayesian Circular Regression with von Mises Quasi-Processes [57.88921637944379]
  In this work we explore a family of expressive and interpretable distributions over circle-valued random functions. For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Gibbs sampling. We present experiments applying this model to the prediction of wind directions and the percentage of the running gait cycle as a function of joint angles.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity [11.71206628091551]
  Diffusion models are costly to train and evaluate, reducing the inference cost for diffusion models remains a major goal. Inspired by the recent empirical success in accelerating diffusion models via the parallel sampling techniqueciteshih2024parallel, we propose to divide the sampling process into $mathcalO(1)$ blocks with parallelizable Picard iterations within each block. Our results shed light on the potential of fast and efficient sampling of high-dimensional data on fast-evolving modern large-memory GPU clusters.
  arXiv  Detail & Related papers  (2024-05-24T23:59:41Z)
• Diffusion posterior sampling for simulation-based inference in tall data settings [53.17563688225137]
  Simulation-based inference ( SBI) is capable of approximating the posterior distribution that relates input parameters to a given observation. In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model. We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost.
  arXiv  Detail & Related papers  (2024-04-11T09:23:36Z)
• Sample-Efficient "Clustering and Conquer" Procedures for Parallel Large-Scale Ranking and Selection [3.913403111891027]
  We modify the commonly used "divide and conquer" framework in parallel computing by adding a correlation-based clustering step.<n>This seemingly simple modification yields an $mathcalO(p)$ reduction in sample complexity for a widely used class of sample-optimal R&S procedures.<n>In large-scale AI applications such as neural architecture search, our methods demonstrate superior performance.
  arXiv  Detail & Related papers  (2024-02-03T15:56:03Z)
• Stochastic Optimization for Non-convex Problem with Inexact Hessian Matrix, Gradient, and Function [99.31457740916815]
  Trust-region (TR) and adaptive regularization using cubics have proven to have some very appealing theoretical properties. We show that TR and ARC methods can simultaneously provide inexact computations of the Hessian, gradient, and function values.
  arXiv  Detail & Related papers  (2023-10-18T10:29:58Z)
• Probabilistic Unrolling: Scalable, Inverse-Free Maximum Likelihood Estimation for Latent Gaussian Models [69.22568644711113]
  We introduce probabilistic unrolling, a method that combines Monte Carlo sampling with iterative linear solvers to circumvent matrix inversions. Our theoretical analyses reveal that unrolling and backpropagation through the iterations of the solver can accelerate gradient estimation for maximum likelihood estimation. In experiments on simulated and real data, we demonstrate that probabilistic unrolling learns latent Gaussian models up to an order of magnitude faster than gradient EM, with minimal losses in model performance.
  arXiv  Detail & Related papers  (2023-06-05T21:08:34Z)
• Generative modeling of time-dependent densities via optimal transport and projection pursuit [3.069335774032178]
  We propose a cheap alternative to popular deep learning algorithms for temporal modeling. Our method is highly competitive compared with state-of-the-art solvers.
  arXiv  Detail & Related papers  (2023-04-19T13:50:13Z)
• Neural Posterior Estimation with Differentiable Simulators [58.720142291102135]
  We present a new method to perform Neural Posterior Estimation (NPE) with a differentiable simulator. We demonstrate how gradient information helps constrain the shape of the posterior and improves sample-efficiency.
  arXiv  Detail & Related papers  (2022-07-12T16:08:04Z)
• Faster One-Sample Stochastic Conditional Gradient Method for Composite Convex Minimization [61.26619639722804]
  We propose a conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. The proposed method, equipped with an average gradient (SAG) estimator, requires only one sample per iteration. Nevertheless, it guarantees fast convergence rates on par with more sophisticated variance reduction techniques.
  arXiv  Detail & Related papers  (2022-02-26T19:10:48Z)
• Heavy-tailed Streaming Statistical Estimation [58.70341336199497]
  We consider the task of heavy-tailed statistical estimation given streaming $p$ samples. We design a clipped gradient descent and provide an improved analysis under a more nuanced condition on the noise of gradients.
  arXiv  Detail & Related papers  (2021-08-25T21:30:27Z)
• Revisiting the Sample Complexity of Sparse Spectrum Approximation of Gaussian Processes [60.479499225746295]
  We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse spectrum Gaussian processes (SSGPs)
  arXiv  Detail & Related papers  (2020-11-17T05:41:50Z)
• Non-Adaptive Adaptive Sampling on Turnstile Streams [57.619901304728366]
  We give the first relative-error algorithms for column subset selection, subspace approximation, projective clustering, and volume on turnstile streams that use space sublinear in $n$. Our adaptive sampling procedure has a number of applications to various data summarization problems that either improve state-of-the-art or have only been previously studied in the more relaxed row-arrival model.
  arXiv  Detail & Related papers  (2020-04-23T05:00:21Z)
• Ensemble Slice Sampling: Parallel, black-box and gradient-free inference for correlated & multimodal distributions [0.0]
  Slice Sampling has emerged as a powerful Markov Chain Monte Carlo algorithm that adapts to the characteristics of the target distribution with minimal hand-tuning. This paper introduces Ensemble Slice Sampling (ESS), a new class of algorithms that bypasses such difficulties by adaptively tuning the initial length scale. These affine-invariant algorithms are trivial to construct, require no hand-tuning, and can easily be implemented in parallel computing environments.
  arXiv  Detail & Related papers  (2020-02-14T19:00:12Z)
• Accelerating Feedforward Computation via Parallel Nonlinear Equation Solving [106.63673243937492]
  Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. We frame the task of feedforward computation as solving a system of nonlinear equations. We then propose to find the solution using a Jacobi or Gauss-Seidel fixed-point method, as well as hybrid methods of both. Our method is guaranteed to give exactly the same values as the original feedforward computation with a reduced (or equal) number of parallelizable iterations, and hence reduced time given sufficient parallel computing power.
  arXiv  Detail & Related papers  (2020-02-10T10:11:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.