Reverse Markov Learning: Multi-Step Generative Models for Complex Distributions

• URL: http://arxiv.org/abs/2502.13747v2
• Date: Mon, 18 Aug 2025 07:48:27 GMT
• Title: Reverse Markov Learning: Multi-Step Generative Models for Complex Distributions
• Authors: Xinwei Shen, Nicolai Meinshausen, Tong Zhang,
• Abstract summary: We propose a framework that defines a general forward process transitioning from the target distribution to a known distribution.<n>We then learn a reverse Markov process using multiple engression models.<n>This framework accommodates general forward processes, allows for dimension reduction, and naturally discretizes the generative process.
• Score: 10.165179181394755
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Learning complex distributions is a fundamental challenge in contemporary applications. Shen and Meinshausen (2024) introduced engression, a generative approach based on scoring rules that maps noise (and covariates, if available) directly to data. While effective, engression can struggle with highly complex distributions, such as those encountered in image data. In this work, we propose reverse Markov learning (RML), a framework that defines a general forward process transitioning from the target distribution to a known distribution (e.g., Gaussian) and then learns a reverse Markov process using multiple engression models. This reverse process reconstructs the target distribution step by step. This framework accommodates general forward processes, allows for dimension reduction, and naturally discretizes the generative process. In the special case of diffusion-based forward processes, RML provides an efficient discretization strategy for both training and inference in diffusion models. We further introduce an alternating sampling scheme to enhance post-training performance. Our statistical analysis establishes error bounds for RML and elucidates its advantages in estimation efficiency and flexibility in forward process design. Empirical results on simulated and climate data corroborate the theoretical findings, demonstrating the effectiveness of RML in capturing complex distributions.

Related papers

• An Elementary Approach to Scheduling in Generative Diffusion Models [55.171367482496755]
  An elementary approach to characterizing the impact of noise scheduling and time discretization in generative diffusion models is developed.<n> Experiments across different datasets and pretrained models demonstrate that the time discretization strategy selected by our approach consistently outperforms baseline and search-based strategies.
  arXiv  Detail & Related papers  (2026-01-20T05:06:26Z)
• Sampling by averaging: A multiscale approach to score estimation [4.003851730099099]
  We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics.<n>Two algorithms are developed: MultALMC and MultCDiff, based on multiscale controlled diffusions for the reverse-time Ornstein-Uhlenbeck process.<n>The framework is extended to handle heavy-dimensional target distributions using Student's t-based noise models and tailored fast-process dynamics.
  arXiv  Detail & Related papers  (2025-08-20T21:09:34Z)
• Inference-Time Scaling of Diffusion Language Models with Particle Gibbs Sampling [62.640128548633946]
  We introduce a novel inference-time scaling approach based on particle Gibbs sampling for discrete diffusion models.<n>Our method consistently outperforms prior inference-time strategies on reward-guided text generation tasks.
  arXiv  Detail & Related papers  (2025-07-11T08:00:47Z)
• Self-Boost via Optimal Retraining: An Analysis via Approximate Message Passing [58.52119063742121]
  Retraining a model using its own predictions together with the original, potentially noisy labels is a well-known strategy for improving the model performance.<n>This paper addresses the question of how to optimally combine the model's predictions and the provided labels.<n>Our main contribution is the derivation of the Bayes optimal aggregator function to combine the current model's predictions and the given labels.
  arXiv  Detail & Related papers  (2025-05-21T07:16:44Z)
• Generalized Interpolating Discrete Diffusion [65.74168524007484]
  Masked diffusion is a popular choice due to its simplicity and effectiveness. We derive the theoretical backbone of a family of general interpolating discrete diffusion processes. Exploiting GIDD's flexibility, we explore a hybrid approach combining masking and uniform noise.
  arXiv  Detail & Related papers  (2025-03-06T14:30:55Z)
• RDPM: Solve Diffusion Probabilistic Models via Recurrent Token Prediction [17.005198258689035]
  Diffusion Probabilistic Models (DPMs) have emerged as the de facto approach for high-fidelity image synthesis.<n>We introduce a novel generative framework, the Recurrent Diffusion Probabilistic Model (RDPM), which enhances the diffusion process through a recurrent token prediction mechanism.
  arXiv  Detail & Related papers  (2024-12-24T12:28:19Z)
• A solvable generative model with a linear, one-step denoiser [0.0]
  We develop an analytically tractable single-step diffusion model based on a linear denoiser.<n>We show that the monotonic fall phase of Kullback-Leibler divergence begins when the training dataset size reaches the dimension of the data points.
  arXiv  Detail & Related papers  (2024-11-26T19:00:01Z)
• Learned Reference-based Diffusion Sampling for multi-modal distributions [2.1383136715042417]
  We introduce Learned Reference-based Diffusion Sampler (LRDS), a methodology specifically designed to leverage prior knowledge on the location of the target modes. LRDS proceeds in two steps by learning a reference diffusion model on samples located in high-density space regions. We experimentally demonstrate that LRDS best exploits prior knowledge on the target distribution compared to competing algorithms on a variety of challenging distributions.
  arXiv  Detail & Related papers  (2024-10-25T10:23:34Z)
• Conditional sampling within generative diffusion models [12.608803080528142]
  We present a review of existing computational approaches to conditional sampling within generative diffusion models.<n>We highlight key methodologies that either utilise the joint distribution, or rely on (pre-trained) marginal distributions with explicit likelihoods.
  arXiv  Detail & Related papers  (2024-09-15T07:48:40Z)
• Reward-Directed Score-Based Diffusion Models via q-Learning [8.725446812770791]
  We propose a new reinforcement learning (RL) formulation for training continuous-time score-based diffusion models for generative AI. Our formulation does not involve any pretrained model for the unknown score functions of the noise-perturbed data distributions.
  arXiv  Detail & Related papers  (2024-09-07T13:55:45Z)
• Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding [84.3224556294803]
  Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences. We aim to optimize downstream reward functions while preserving the naturalness of these design spaces. Our algorithm integrates soft value functions, which looks ahead to how intermediate noisy states lead to high rewards in the future.
  arXiv  Detail & Related papers  (2024-08-15T16:47:59Z)
• Variational Learning of Gaussian Process Latent Variable Models through Stochastic Gradient Annealed Importance Sampling [22.256068524699472]
  In this work, we propose an Annealed Importance Sampling (AIS) approach to address these issues. We combine the strengths of Sequential Monte Carlo samplers and VI to explore a wider range of posterior distributions and gradually approach the target distribution. Experimental results on both toy and image datasets demonstrate that our method outperforms state-of-the-art methods in terms of tighter variational bounds, higher log-likelihoods, and more robust convergence.
  arXiv  Detail & Related papers  (2024-08-13T08:09:05Z)
• Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Review [63.31328039424469]
  This tutorial provides a comprehensive survey of methods for fine-tuning diffusion models to optimize downstream reward functions. We explain the application of various RL algorithms, including PPO, differentiable optimization, reward-weighted MLE, value-weighted sampling, and path consistency learning.
  arXiv  Detail & Related papers  (2024-07-18T17:35:32Z)
• Diffusion Spectral Representation for Reinforcement Learning [17.701625371409644]
  We propose to leverage the flexibility of diffusion models for reinforcement learning from a representation learning perspective. By exploiting the connection between diffusion models and energy-based models, we develop Diffusion Spectral Representation (Diff-SR) We show how Diff-SR facilitates efficient policy optimization and practical algorithms while explicitly bypassing the difficulty and inference cost of sampling from the diffusion model.
  arXiv  Detail & Related papers  (2024-06-23T14:24:14Z)
• Training Implicit Generative Models via an Invariant Statistical Loss [3.139474253994318]
  Implicit generative models have the capability to learn arbitrary complex data distributions. On the downside, training requires telling apart real data from artificially-generated ones using adversarial discriminators. We develop a discriminator-free method for training one-dimensional (1D) generative implicit models.
  arXiv  Detail & Related papers  (2024-02-26T09:32:28Z)
• Broadening Target Distributions for Accelerated Diffusion Models via a Novel Analysis Approach [49.97755400231656]
  We show that a novel accelerated DDPM sampler achieves accelerated performance for three broad distribution classes not considered before. Our results show an improved dependency on the data dimension $d$ among accelerated DDPM type samplers.
  arXiv  Detail & Related papers  (2024-02-21T16:11:47Z)
• Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformization [17.535229185525353]
  We introduce an algorithm leveraging the uniformization of continuous Markov chains, implementing transitions on random time points. Our results align with state-of-the-art achievements for diffusion models in $mathbbRd$ and further underscore the advantages of discrete diffusion models in comparison to the $mathbbRd$ setting.
  arXiv  Detail & Related papers  (2024-02-12T22:26:52Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Generative Modeling on Manifolds Through Mixture of Riemannian Diffusion Processes [57.396578974401734]
  We introduce a principled framework for building a generative diffusion process on general manifold. Instead of following the denoising approach of previous diffusion models, we construct a diffusion process using a mixture of bridge processes. We develop a geometric understanding of the mixture process, deriving the drift as a weighted mean of tangent directions to the data points.
  arXiv  Detail & Related papers  (2023-10-11T06:04:40Z)
• Distributionally Robust Model-based Reinforcement Learning with Large State Spaces [55.14361269378122]
  Three major challenges in reinforcement learning are the complex dynamical systems with large state spaces, the costly data acquisition processes, and the deviation of real-world dynamics from the training environment deployment. We study distributionally robust Markov decision processes with continuous state spaces under the widely used Kullback-Leibler, chi-square, and total variation uncertainty sets. We propose a model-based approach that utilizes Gaussian Processes and the maximum variance reduction algorithm to efficiently learn multi-output nominal transition dynamics.
  arXiv  Detail & Related papers  (2023-09-05T13:42:11Z)
• Reflected Diffusion Models [93.26107023470979]
  We present Reflected Diffusion Models, which reverse a reflected differential equation evolving on the support of the data. Our approach learns the score function through a generalized score matching loss and extends key components of standard diffusion models.
  arXiv  Detail & Related papers  (2023-04-10T17:54:38Z)
• Distributionally Robust Models with Parametric Likelihood Ratios [123.05074253513935]
  Three simple ideas allow us to train models with DRO using a broader class of parametric likelihood ratios. We find that models trained with the resulting parametric adversaries are consistently more robust to subpopulation shifts when compared to other DRO approaches.
  arXiv  Detail & Related papers  (2022-04-13T12:43:12Z)
• Sampling from Arbitrary Functions via PSD Models [55.41644538483948]
  We take a two-step approach by first modeling the probability distribution and then sampling from that model. We show that these models can approximate a large class of densities concisely using few evaluations, and present a simple algorithm to effectively sample from these models.
  arXiv  Detail & Related papers  (2021-10-20T12:25:22Z)

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.