Telegrapher's Generative Model via Kac Flows

• URL: http://arxiv.org/abs/2506.20641v3
• Date: Tue, 05 Aug 2025 00:49:40 GMT
• Title: Telegrapher's Generative Model via Kac Flows
• Authors: Richard Duong, Jannis Chemseddine, Peter K. Friz, Gabriele Steidl,
• Abstract summary: We propose a new flow-based generative model based on the damped wave equation, also known as telegrapher's equation.<n>Using the framework of flow matching, we train a neural network that approximates the velocity field and use it for sample generation.
• Score: 1.2499537119440245
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We break the mold in flow-based generative modeling by proposing a new model based on the damped wave equation, also known as telegrapher's equation. Similar to the diffusion equation and Brownian motion, there is a Feynman-Kac type relation between the telegrapher's equation and the stochastic Kac process in 1D. The Kac flow evolves stepwise linearly in time, so that the probability flow is Lipschitz continuous in the Wasserstein distance and, in contrast to diffusion flows, the norm of the velocity is globally bounded. Furthermore, the Kac model has the diffusion model as its asymptotic limit. We extend these considerations to a multi-dimensional stochastic process which consists of independent 1D Kac processes in each spatial component. We show that this process gives rise to an absolutely continuous curve in the Wasserstein space and compute the conditional velocity field starting in a Dirac point analytically. Using the framework of flow matching, we train a neural network that approximates the velocity field and use it for sample generation. Our numerical experiments demonstrate the scalability of our approach, and show its advantages over diffusion models.

Related papers

• FlowDPS: Flow-Driven Posterior Sampling for Inverse Problems [51.99765487172328]
  Posterior sampling for inverse problem solving can be effectively achieved using flows.<n>Flow-Driven Posterior Sampling (FlowDPS) outperforms state-of-the-art alternatives.
  arXiv  Detail & Related papers  (2025-03-11T07:56:14Z)
• Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans [1.9766522384767222]
  Flow matching techniques can be used to solve inverse problems.<n>We show how flow matching can be used for solving inverse problems.<n>We briefly address continuous normalizing flows and score matching techniques.
  arXiv  Detail & Related papers  (2025-01-28T10:28:17Z)
• 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.<n>For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Gibbs sampling.<n>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)
• Neural Sinkhorn Gradient Flow [11.4522103360875]
  We introduce the Neural Sinkhorn Gradient Flow (NSGF) model, which parametrizes the time-varying velocity field of the Wasserstein gradient flow. Our theoretical analyses show that as the sample size increases to infinity, the mean-field limit of the empirical approximation converges to the true underlying velocity field. To further enhance model efficiency on high-dimensional tasks, a two-phase NSGF++ model is devised.
  arXiv  Detail & Related papers  (2024-01-25T10:44:50Z)
• DiffuSeq-v2: Bridging Discrete and Continuous Text Spaces for Accelerated Seq2Seq Diffusion Models [58.450152413700586]
  We introduce a soft absorbing state that facilitates the diffusion model in learning to reconstruct discrete mutations based on the underlying Gaussian space. We employ state-of-the-art ODE solvers within the continuous space to expedite the sampling process. Our proposed method effectively accelerates the training convergence by 4x and generates samples of similar quality 800x faster.
  arXiv  Detail & Related papers  (2023-10-09T15:29:10Z)
• On the path integral simulation of space-time fractional Schroedinger equation with time independent potentials [0.0]
  A Feynman-Kac path integral method has been proposed for solving the Cauchy problems associated with the space-time fractional Schroedinger equations. We have been able to simulate the space-time fractional diffusion process with comparable simplicity and convergence rate as in the case of a standard diffusion.
  arXiv  Detail & Related papers  (2023-06-25T20:14:40Z)
• Lipschitz Singularities in Diffusion Models [64.28196620345808]
  Diffusion models often display the infinite Lipschitz property of the network with respect to time variable near the zero point.<n>We propose a novel approach, dubbed E-TSDM, which alleviates the Lipschitz singularities of the diffusion model near the zero point.<n>Our work may advance the understanding of the general diffusion process, and also provide insights for the design of diffusion models.
  arXiv  Detail & Related papers  (2023-06-20T03:05:28Z)
• A Geometric Perspective on Diffusion Models [57.27857591493788]
  We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
  arXiv  Detail & Related papers  (2023-05-31T15:33:16Z)
• 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)
• Fast Sampling of Diffusion Models via Operator Learning [74.37531458470086]
  We use neural operators, an efficient method to solve the probability flow differential equations, to accelerate the sampling process of diffusion models. Compared to other fast sampling methods that have a sequential nature, we are the first to propose a parallel decoding method. We show our method achieves state-of-the-art FID of 3.78 for CIFAR-10 and 7.83 for ImageNet-64 in the one-model-evaluation setting.
  arXiv  Detail & Related papers  (2022-11-24T07:30:27Z)
• A blob method method for inhomogeneous diffusion with applications to multi-agent control and sampling [0.6562256987706128]
  We develop a deterministic particle method for the weighted porous medium equation (WPME) and prove its convergence on bounded time intervals. Our method has natural applications to multi-agent coverage algorithms and sampling probability measures.
  arXiv  Detail & Related papers  (2022-02-25T19:49:05Z)

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.