Discrete Markov Probabilistic Models

• URL: http://arxiv.org/abs/2502.07939v1
• Date: Tue, 11 Feb 2025 20:36:23 GMT
• Title: Discrete Markov Probabilistic Models
• Authors: Le-Tuyet-Nhi Pham, Dario Shariatian, Antonio Ocello, Giovanni Conforti, Alain Durmus,
• Abstract summary: The Discrete Markov Probabilistic Model (DMPM) is a novel algorithm for discrete data generation. The intensity of the time-reversal process is governed by a discrete analogue of the classical score function. This work bridges theoretical foundations and practical applications, advancing the development of effective and theoretically grounded discrete generative modeling.
• Score: 8.206838934494513
• License:
• Abstract: This paper introduces the Discrete Markov Probabilistic Model (DMPM), a novel algorithm for discrete data generation. The algorithm operates in the space of bits $\{0,1\}^d$, where the noising process is a continuous-time Markov chain that can be sampled exactly via a Poissonian clock that flips labels uniformly at random. The time-reversal process, like the forward noise process, is a jump process, with its intensity governed by a discrete analogue of the classical score function. Crucially, this intensity is proven to be the conditional expectation of a function of the forward process, strengthening its theoretical alignment with score-based generative models while ensuring robustness and efficiency. We further establish convergence bounds for the algorithm under minimal assumptions and demonstrate its effectiveness through experiments on low-dimensional Bernoulli-distributed datasets and high-dimensional binary MNIST data. The results highlight its strong performance in generating discrete structures. This work bridges theoretical foundations and practical applications, advancing the development of effective and theoretically grounded discrete generative modeling.

Related papers

• Flow-based generative models as iterative algorithms in probability space [18.701755188870823]
  Flow-based generative models offer exact likelihood estimation, efficient sampling, and deterministic transformations. This tutorial presents an intuitive mathematical framework for flow-based generative models. We aim to equip researchers and practitioners with the necessary tools to effectively apply flow-based generative models in signal processing and machine learning.
  arXiv  Detail & Related papers  (2025-02-19T03:09:18Z)
• 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. 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)
• Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis [56.442307356162864]
  We study the theoretical aspects of score-based discrete diffusion models under the Continuous Time Markov Chain (CTMC) framework. We introduce a discrete-time sampling algorithm in the general state space $[S]d$ that utilizes score estimators at predefined time points. Our convergence analysis employs a Girsanov-based method and establishes key properties of the discrete score function.
  arXiv  Detail & Related papers  (2024-10-03T09:07:13Z)
• BGDB: Bernoulli-Gaussian Decision Block with Improved Denoising Diffusion Probabilistic Models [8.332734198630813]
  Generative models can enhance discriminative classifiers by constructing complex feature spaces. We propose the Bernoulli-Gaussian Decision Block (BGDB), a novel module inspired by the Central Limit Theorem. Specifically, we utilize Improved Denoising Diffusion Probabilistic Models (IDDPM) to model the probability of Bernoulli Trials.
  arXiv  Detail & Related papers  (2024-09-19T22:52:55Z)
• On the Trajectory Regularity of ODE-based Diffusion Sampling [79.17334230868693]
  Diffusion-based generative models use differential equations to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models.
  arXiv  Detail & Related papers  (2024-05-18T15:59:41Z)
• 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)
• ChiroDiff: Modelling chirographic data with Diffusion Models [132.5223191478268]
  We introduce a powerful model-class namely "Denoising Diffusion Probabilistic Models" or DDPMs for chirographic data. Our model named "ChiroDiff", being non-autoregressive, learns to capture holistic concepts and therefore remains resilient to higher temporal sampling rate.
  arXiv  Detail & Related papers  (2023-04-07T15:17:48Z)
• Score-based Continuous-time Discrete Diffusion Models [102.65769839899315]
  We extend diffusion models to discrete variables by introducing a Markov jump process where the reverse process denoises via a continuous-time Markov chain. We show that an unbiased estimator can be obtained via simple matching the conditional marginal distributions. We demonstrate the effectiveness of the proposed method on a set of synthetic and real-world music and image benchmarks.
  arXiv  Detail & Related papers  (2022-11-30T05:33:29Z)
• The Boomerang Sampler [4.588028371034406]
  This paper introduces the Boomerang Sampler as a novel class of continuous-time non-reversible Markov chain Monte Carlo algorithms. We demonstrate that the method is easy to implement and demonstrate empirically that it can out-perform existing benchmark piecewise deterministic Markov processes.
  arXiv  Detail & Related papers  (2020-06-24T14:52:22Z)
• Multiplicative noise and heavy tails in stochastic optimization [62.993432503309485]
  empirical optimization is central to modern machine learning, but its role in its success is still unclear. We show that it commonly arises in parameters of discrete multiplicative noise due to variance. A detailed analysis is conducted in which we describe on key factors, including recent step size, and data, all exhibit similar results on state-of-the-art neural network models.
  arXiv  Detail & Related papers  (2020-06-11T09:58:01Z)

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.