Latent Process Generator Matching

• URL: http://arxiv.org/abs/2605.20547v1
• Date: Tue, 19 May 2026 22:49:05 GMT
• Title: Latent Process Generator Matching
• Abstract summary: We introduce latent process generator matching, a general framework that treats the observed generative state as a deterministic image.<n>We show that in this setting one may learn the generator of a process on the image space which has the same one-time marginal distributions as the projected process.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many recent flow-matching and diffusion-style generative models rely on auxiliary stochastic dynamics during training: a richer process is simulated to define conditional targets, but the auxiliary state is either intractable to sample at generation time or simply not part of the desired output. Existing Generator Matching theory formalises conditioning on static latent random variables, and several recent papers prove special cases of projection results for particular augmented-state constructions. We introduce latent process generator matching, a general framework that treats the observed generative state as a deterministic image $X_t=Φ(Y_t)$ of a tractable Markov process $Y_t$. We show that in this setting one may learn the generator of a stochastic process on the image space which has the same one-time marginal distributions as the projected process. This generalizes and subsumes the discrete latent process results from the literature, and extends Generator Matching from static latent variables to a rich family of time-dependent latent conditional processes.

Related papers

• Generative Modeling of Approximately Periodic Time Series by a Posterior-Weighted Gaussian Process [0.4460583138505672]
  We propose a generative model for approximately periodic time series.<n>Our approach decouples intra-repetition structure from inter-repetition variability through a two-stage construction.
  arXiv  Detail & Related papers  (2026-05-13T08:17:00Z)
• Discrete Feynman-Kac Correctors [47.62319930071118]
  We propose a framework that allows for controlling the generated distribution of discrete masked diffusion models at inference time.<n>We derive Sequential Monte Carlo (SMC) algorithms that, given a trained discrete diffusion model, control the temperature of the sampled distribution.<n>We illustrate the utility of our framework in several applications including: efficient sampling from the Boltzmann distribution of the Ising model, improving the performance of language models for code generation and amortized learning, as well as reward-tilted protein sequence generation.
  arXiv  Detail & Related papers  (2026-01-15T13:55:38Z)
• Random-Bridges as Stochastic Transports for Generative Models [1.2599533416395763]
  This paper motivates the use of random-bridges -- conditioned processes to take target distributions at fixed time inception.<n>We show how one can start from general probabilistic statements and then branch out into specific representations for learning and simulation algorithms.
  arXiv  Detail & Related papers  (2025-12-16T08:37:19Z)
• Distributional Diffusion Models with Scoring Rules [83.38210785728994]
  Diffusion models generate high-quality synthetic data.<n> generating high-quality outputs requires many discretization steps.<n>We propose to accomplish sample generation by learning the posterior em distribution of clean data samples.
  arXiv  Detail & Related papers  (2025-02-04T16:59:03Z)
• GenFormer: A Deep-Learning-Based Approach for Generating Multivariate Stochastic Processes [5.679243827959339]
  We propose a Transformer-based deep learning model that learns a mapping between a Markov state sequence and time series values. The GenFormer model is applied to simulate synthetic wind speed data at various stations in Florida to calculate exceedance probabilities for risk management.
  arXiv  Detail & Related papers  (2024-02-03T03:50:18Z)
• 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)
• Accurate generation of stochastic dynamics based on multi-model Generative Adversarial Networks [0.0]
  Generative Adversarial Networks (GANs) have shown immense potential in fields such as text and image generation. Here we quantitatively test this approach by applying it to a prototypical process on a lattice. Importantly, the discreteness of the model is retained despite the noise.
  arXiv  Detail & Related papers  (2023-05-25T10:41:02Z)
• Symbolic Music Generation with Diffusion Models [4.817429789586127]
  We present a technique for training diffusion models on sequential data by parameterizing the discrete domain in the continuous latent space of a pre-trained variational autoencoder. We show strong unconditional generation and post-hoc conditional infilling results compared to autoregressive language models operating over the same continuous embeddings.
  arXiv  Detail & Related papers  (2021-03-30T05:48:05Z)
• Pathwise Conditioning of Gaussian Processes [72.61885354624604]
  Conventional approaches for simulating Gaussian process posteriors view samples as draws from marginal distributions of process values at finite sets of input locations. This distribution-centric characterization leads to generative strategies that scale cubically in the size of the desired random vector. We show how this pathwise interpretation of conditioning gives rise to a general family of approximations that lend themselves to efficiently sampling Gaussian process posteriors.
  arXiv  Detail & Related papers  (2020-11-08T17:09:37Z)
• Conditional Hybrid GAN for Sequence Generation [56.67961004064029]
  We propose a novel conditional hybrid GAN (C-Hybrid-GAN) to solve this issue. We exploit the Gumbel-Softmax technique to approximate the distribution of discrete-valued sequences. We demonstrate that the proposed C-Hybrid-GAN outperforms the existing methods in context-conditioned discrete-valued sequence generation.
  arXiv  Detail & Related papers  (2020-09-18T03:52:55Z)
• Efficiently Sampling Functions from Gaussian Process Posteriors [76.94808614373609]
  We propose an easy-to-use and general-purpose approach for fast posterior sampling. We demonstrate how decoupled sample paths accurately represent Gaussian process posteriors at a fraction of the usual cost.
  arXiv  Detail & Related papers  (2020-02-21T14:03:16Z)

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.