Simulation-free and finite-time diffusion model

• URL: http://arxiv.org/abs/2608.03117v1
• Date: Tue, 04 Aug 2026 04:39:14 GMT
• Title: Simulation-free and finite-time diffusion model
• Abstract summary: We propose a framework for designing the reference process that achieves both simultaneously.<n>We show that conditional flow matching arises as the small-noise limit of the proposed framework.
• Score: 0.688204255655161
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The performance of generative diffusion models is determined by the choice of the reference diffusion process connecting the empirical and prior distributions. Conventional approaches typically trade off simulation-free training against finite-time generation. We propose a framework for designing the reference process that achieves both simultaneously. The key idea is to prescribe tractable time-dependent conditional distributions and then construct the reference process realizing them as its marginals. This framework reveals that score matching is not fundamental to diffusion-model training but instead emerges naturally through reversal of the reference process. We further show that conditional flow matching arises as the small-noise limit of the proposed framework.

Related papers

• A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models [0.3222802562733787]
  We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via deterministic dynamics.<n>We present a unified framework in which diffusion models, score-based generative models, and flow matching are instances of learning a time-dependent vector field.
  arXiv  Detail & Related papers  (2026-05-07T18:32:15Z)
• Accelerated Sequential Flow Matching: A Bayesian Filtering Perspective [16.29333060724397]
  We introduce Sequential Flow Matching, a principled framework grounded in Bayesian filtering.<n>By treating streaming inference as learning a probability flow that transports the predictive distribution from one time step to the next, our approach naturally aligns with the structure of Bayesian belief updates.<n>Our method achieves performance competitive with full-step diffusion while requiring only one or very few sampling steps, therefore with faster sampling.
  arXiv  Detail & Related papers  (2026-02-05T05:37:14Z)
• Effective Test-Time Scaling of Discrete Diffusion through Iterative Refinement [51.54933696252104]
  We introduce Iterative Reward-Guided Refinement (IterRef), a novel test-time scaling method tailored to discrete diffusion.<n>We formalize this process within a Multiple-Try Metropolis framework, proving convergence to the reward-aligned distribution.<n>IterRef achieves striking gains under low compute budgets, far surpassing prior state-of-the-art baselines.
  arXiv  Detail & Related papers  (2025-11-04T02:33:23Z)
• A diffusion-based generative model for financial time series via geometric Brownian motion [1.3654846342364308]
  We propose a novel diffusion-based generative framework for financial time series.<n>Our method injects noise proportionally to asset prices at each time step, reflecting the heteroskedasticity observed in financial time series.<n>By accurately balancing the drift and diffusion terms, we show that the resulting log-price process reduces to a variance-exploding differential equation.
  arXiv  Detail & Related papers  (2025-07-25T07:02:09Z)
• Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generation [0.0]
  dependencies between intermediate noisy states lead to error accumulation and propagation during the reverse denoising process.<n>We propose a novel framework called Simple Iterative Denoising, which simplifies discrete diffusion and circumvents the issue.<n>Our empirical evaluations demonstrate that the proposed method significantly outperforms existing discrete diffusion baselines in graph generation tasks.
  arXiv  Detail & Related papers  (2025-03-27T15:08:58Z)
• Continuous Diffusion Model for Language Modeling [64.7425225935854]
  Existing continuous diffusion models for discrete data underperform compared to discrete methods.<n>We propose a continuous diffusion model for language modeling that incorporates the geometry of the underlying categorical distribution.<n>Our method outperforms existing discrete diffusion models and approaches the performance of autoregressive models.
  arXiv  Detail & Related papers  (2025-02-17T08:54:29Z)
• Accelerated Diffusion Models via Speculative Sampling [89.43940130493233]
  Speculative sampling is a popular technique for accelerating inference in Large Language Models.<n>We extend speculative sampling to diffusion models, which generate samples via continuous, vector-valued Markov chains.<n>We propose various drafting strategies, including a simple and effective approach that does not require training a draft model.
  arXiv  Detail & Related papers  (2025-01-09T16:50:16Z)
• Flow Matching Posterior Sampling: A Training-free Conditional Generation for Flow Matching [13.634043135217254]
  We propose Flow Matching-based Posterior Sampling (FMPS) to expand its application scope.<n>This correction term can be reformulated to incorporate a surrogate score function.<n>We show that FMPS achieves superior generation quality compared to existing state-of-the-art approaches.
  arXiv  Detail & Related papers  (2024-11-12T08:14:39Z)
• Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
  We present the first performance guarantee with explicit dimensional dependencies for general score-mismatched diffusion samplers.<n>We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions.<n>This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
  arXiv  Detail & Related papers  (2024-10-17T16:42:12Z)
• Conditional Lagrangian Wasserstein Flow for Time Series Imputation [3.583527519172841]
  Conditional Lagrangian Wasserstein Flow is a novel method for time series imputation.<n>We learn the velocity by minimizing the corresponding kinetic energy.<n>To enhance the model's performance, we estimate the gradient of a task-specific potential function.
  arXiv  Detail & Related papers  (2024-10-10T02:46:28Z)
• 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)
• Flow map matching with stochastic interpolants: A mathematical framework for consistency models [15.520853806024943]
  Flow Map Matching is a principled framework for learning the two-time flow map of an underlying generative model.<n>We show that FMM unifies and extends a broad class of existing approaches for fast sampling.
  arXiv  Detail & Related papers  (2024-06-11T17:41:26Z)
• Time-series Generation by Contrastive Imitation [87.51882102248395]
  We study a generative framework that seeks to combine the strengths of both: Motivated by a moment-matching objective to mitigate compounding error, we optimize a local (but forward-looking) transition policy. At inference, the learned policy serves as the generator for iterative sampling, and the learned energy serves as a trajectory-level measure for evaluating sample quality.
  arXiv  Detail & Related papers  (2023-11-02T16:45:25Z)
• Towards Recurrent Autoregressive Flow Models [39.25035894474609]
  We present Recurrent Autoregressive Flows as a method toward general process modeling with normalizing flows. The proposed method defines a conditional distribution for each variable in a sequential process by conditioning the parameters of a normalizing flow with recurrent neural connections. We demonstrate the effectiveness of this class of models through a series of experiments in which models are trained on three complex processes.
  arXiv  Detail & Related papers  (2020-06-17T18:38:36Z)
• Composing Normalizing Flows for Inverse Problems [89.06155049265641]
  We propose a framework for approximate inference that estimates the target conditional as a composition of two flow models. Our method is evaluated on a variety of inverse problems and is shown to produce high-quality samples with uncertainty.
  arXiv  Detail & Related papers  (2020-02-26T19:01:11Z)

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.