Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning

• URL: http://arxiv.org/abs/2505.05151v3
• Date: Sun, 29 Jun 2025 15:35:22 GMT
• Title: Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning
• Authors: Chuangtao Chen, Qinglin Zhao, MengChu Zhou, Dusit Niyato, Zhimin He, Haozhen Situ,
• Abstract summary: We propose a quantum Discrete Denoising Diffusion Probabilistic Model (QD3PM)<n>It enables joint probability learning through diffusion and denoising in exponentially large Hilbert spaces.<n>This paper establishes a new theoretical paradigm in generative models by leveraging the quantum advantage in joint distribution learning.
• Score: 79.65014491424151
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Discrete diffusion models represent a significant advance in generative modeling, demonstrating remarkable success in synthesizing complex, high-quality discrete data. However, to avoid exponential computational costs, they typically rely on calculating per-dimension transition probabilities when learning high-dimensional distributions. In this study, we rigorously prove that this approach leads to a worst-case linear scaling of Kullback-Leibler (KL) divergence with data dimension. To address this, we propose a Quantum Discrete Denoising Diffusion Probabilistic Model (QD3PM), which enables joint probability learning through diffusion and denoising in exponentially large Hilbert spaces, offering a theoretical pathway to faithfully capture the true joint distribution. By deriving posterior states through quantum Bayes' theorem, similar to the crucial role of posterior probabilities in classical diffusion models, and by learning the joint probability, we establish a solid theoretical foundation for quantum-enhanced diffusion models. For denoising, we design a quantum circuit that utilizes temporal information for parameter sharing and incorporates learnable classical-data-controlled rotations for encoding. Exploiting joint distribution learning, our approach enables single-step sampling from pure noise, eliminating iterative requirements of existing models. Simulations demonstrate the proposed model's superior accuracy in modeling complex distributions compared to factorization methods. Hence, this paper establishes a new theoretical paradigm in generative models by leveraging the quantum advantage in joint distribution learning.

Related papers

• Generative Latent Neural PDE Solver using Flow Matching [8.397730500554047]
  We propose a latent diffusion model for PDE simulation that embeds the PDE state in a lower-dimensional latent space.<n>Our framework uses an autoencoder to map different types of meshes onto a unified structured latent grid, capturing complex geometries.<n> Numerical experiments show that the proposed model outperforms several deterministic baselines in both accuracy and long-term stability.
  arXiv  Detail & Related papers  (2025-03-28T16:44:28Z)
• Generalized Diffusion Model with Adjusted Offset Noise [1.7767466724342067]
  We propose a generalized diffusion model that naturally incorporates additional noise within a rigorous probabilistic framework.<n>We derive a loss function based on the evidence lower bound, establishing its theoretical equivalence to offset noise with certain adjustments.<n>Experiments on synthetic datasets demonstrate that our model effectively addresses brightness-related challenges and outperforms conventional methods in high-dimensional scenarios.
  arXiv  Detail & Related papers  (2024-12-04T08:57:03Z)
• How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Framework [11.71206628091551]
  We propose a comprehensive framework for the error analysis of discrete diffusion models based on L'evy-type integrals.<n>Our framework unifies and strengthens the current theoretical results on discrete diffusion models.
  arXiv  Detail & Related papers  (2024-10-04T16:59:29Z)
• 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.<n>We introduce a discrete-time sampling algorithm in the general state space $[S]d$ that utilizes score estimators at predefined time points.<n>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)
• Constrained Diffusion Models via Dual Training [80.03953599062365]
  Diffusion processes are prone to generating samples that reflect biases in a training dataset. We develop constrained diffusion models by imposing diffusion constraints based on desired distributions. We show that our constrained diffusion models generate new data from a mixture data distribution that achieves the optimal trade-off among objective and constraints.
  arXiv  Detail & Related papers  (2024-08-27T14:25:42Z)
• Predicting Cascading Failures with a Hyperparametric Diffusion Model [66.89499978864741]
  We study cascading failures in power grids through the lens of diffusion models. Our model integrates viral diffusion principles with physics-based concepts. We show that this diffusion model can be learned from traces of cascading failures.
  arXiv  Detail & Related papers  (2024-06-12T02:34:24Z)
• Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory [87.00653989457834]
  Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. Despite the empirical success, theory of conditional diffusion models is largely missing. This paper bridges the gap by presenting a sharp statistical theory of distribution estimation using conditional diffusion models.
  arXiv  Detail & Related papers  (2024-03-18T17:08:24Z)
• Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Models [59.331993845831946]
  Diffusion models benefit from instillation of task-specific information into the score function to steer the sample generation towards desired properties. This paper provides the first theoretical study towards understanding the influence of guidance on diffusion models in the context of Gaussian mixture models.
  arXiv  Detail & Related papers  (2024-03-03T23:15:48Z)
• Broadening Target Distributions for Accelerated Diffusion Models via a Novel Analysis Approach [49.97755400231656]
  We show that a new accelerated DDPM sampler achieves accelerated performance for three broad distribution classes not considered before.<n>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)
• On Error Propagation of Diffusion Models [77.91480554418048]
  We develop a theoretical framework to mathematically formulate error propagation in the architecture of DMs. We apply the cumulative error as a regularization term to reduce error propagation. Our proposed regularization reduces error propagation, significantly improves vanilla DMs, and outperforms previous baselines.
  arXiv  Detail & Related papers  (2023-08-09T15:31:17Z)
• Kernel Density Matrices for Probabilistic Deep Learning [8.486487001779416]
  In quantum mechanics, a density matrix is the most general way to describe the state of a quantum system. This paper introduces a novel approach to probabilistic deep learning, kernel density matrices. It provides a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random variables.
  arXiv  Detail & Related papers  (2023-05-26T12:59:58Z)
• Information-Theoretic Diffusion [18.356162596599436]
  Denoising diffusion models have spurred significant gains in density modeling and image generation. We introduce a new mathematical foundation for diffusion models inspired by classic results in information theory.
  arXiv  Detail & Related papers  (2023-02-07T23:03:07Z)
• An optimal control perspective on diffusion-based generative modeling [9.806130366152194]
  We establish a connection between optimal control and generative models based on differential equations (SDEs) In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals. We develop a novel diffusion-based method for sampling from unnormalized densities.
  arXiv  Detail & Related papers  (2022-11-02T17:59:09Z)

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.