Memory-Conditioned Diffusion Model for Generalized Langevin Dynamics
Abstract
Generalized Langevin equations describe non-Markovian dynamics in which the evolution of resolved variables depends on their past. We propose a memory-conditioned diffusion method for learning stochastic flow maps of these dynamics from observed trajectories, without identifying a memory kernel or reconstructing unresolved variables. A compact, recursively updated bank of exponential filters enables the flow map to retain predictive history over multiple time scales without conditioning on long observation windows. The next-step distribution is conditioned on the current observation and this memory state, whose storage and update costs are independent of the history length for a fixed bank size. Predictive criteria guide the memory budget, with reference-assisted selection in the vector benchmark, and an optional linear projection further reduces the conditioning dimension. A kernel-based score estimator generates conditional samples without training a score network, and these samples are used to train a neural flow map for autoregressive simulation. Three numerical examples assess long-memory retention at small conditioning dimension, predictive compression in coupled vector dynamics, and non-Gaussian conditional distributions and intermittent events. The non-Gaussian example reproduces conditional asymmetry and burst statistics in a stochastic model of the plasma scrape-off layer.
Related
- History-Conditioned Inference of Memory and Stochastic Forcing in Generalized Langevin Equations under Lévy Noise
- Optimal Scaling of Langevin Proposals with Generalized Acceptance Rules
- Diffusion Removes Langevin's Conditioning Dependence: A Sharp Gaussian Analysis
- Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
- SULA: Robust Langevin Sampling via Drift-Diffusion Saturation
BibTeX
@misc{yang2026memoryconditioned,
title = {{Memory-Conditioned Diffusion Model for Generalized Langevin Dynamics}},
author = {Minglei Yang and Sicheng He},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28371},
eprint = {2609.28371},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28371},
}
RIS
TY - UNPB
TI - Memory-Conditioned Diffusion Model for Generalized Langevin Dynamics
AU - Minglei Yang
AU - Sicheng He
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28371
UR - https://arxiv.org/abs/2609.28371
AB - Generalized Langevin equations describe non-Markovian dynamics in which the evolution of resolved variables depends on their past. We propose a memory-conditioned diffusion method for learning stochastic flow maps of these dynamics from observed trajectories, without identifying a memory kernel or reconstructing unresolved variables. A compact, recursively updated bank of exponential filters enables the flow map to retain predictive history over multiple time scales without conditioning on long observation windows. The next-step distribution is conditioned on the current observation and this memory state, whose storage and update costs are independent of the history length for a fixed bank size. Predictive criteria guide the memory budget, with reference-assisted selection in the vector benchmark, and an optional linear projection further reduces the conditioning dimension. A kernel-based score estimator generates conditional samples without training a score network, and these samples are used to train a neural flow map for autoregressive simulation. Three numerical examples assess long-memory retention at small conditioning dimension, predictive compression in coupled vector dynamics, and non-Gaussian conditional distributions and intermittent events. The non-Gaussian example reproduces conditional asymmetry and burst statistics in a stochastic model of the plasma scrape-off layer.
ER -