Related papers: On Forgetting and Stability of Score-based Generat…

In this paper we consider the global qualitative properties of a stochastically perturbed logistic model of population growth. In this model, the stochastic perturbations are assumed to be of the white noise type and are proportional to the…

Given the ease of creating synthetic data from machine learning models, new models can be potentially trained on synthetic data generated by previous models. This recursive training process raises concerns about the long-term impact on…

Markov chain Monte Carlo methods are central in computational statistics, and typically rely on detailed balance to ensure invariance with respect to a target distribution. Although straightforward to construct by Metropolization, this can…

The Markov property is widely imposed in analysis of time series data. Correspondingly, testing the Markov property, and relatedly, inferring the order of a Markov model, are of paramount importance. In this article, we propose a…

We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…

We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles. We introduce a model in which visible and hidden variables interact through two…

One of the major challenges in neuroscience is to determine how noise that is present at the molecular and cellular levels affects dynamics and information processing at the macroscopic level of synaptically coupled neuronal populations.…

Discrete flow models offer a powerful framework for learning distributions over discrete state spaces and have demonstrated superior performance compared to the discrete diffusion models. However, their convergence properties and error…

A central challenge faced by memory systems is the robust retrieval of a stored pattern in the presence of interference due to other stored patterns and noise. A theoretically well-founded solution to robust retrieval is given by attractor…

Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…

Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…

Markov chains and diffusion processes are indispensable tools in machine learning and statistics that are used for inference, sampling, and modeling. With the growth of large-scale datasets, the computational cost associated with simulating…

Denoising diffusion models are a class of generative models which have recently achieved state-of-the-art results across many domains. Gradual noise is added to the data using a diffusion process, which transforms the data distribution into…

Chaotic dynamical systems exhibit strong sensitivity to initial conditions and often contain unresolved multiscale processes, making deterministic forecasting fundamentally limited. Generative models offer an appealing alternative by…

We propose a new score-based model with one-step sampling. Previously, score-based models were burdened with heavy computations due to iterative sampling. For substituting the iterative process, we train a standalone generator to compress…

Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse…

Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…

Diffusion models generate samples by denoising along the score of a perturbed target distribution. In practice, one trains a neural diffusion model, which is computationally expensive. Recent work suggests that score matching implicitly…

The nervous system reorganizes memories from an early site to a late site, a commonly observed feature of learning and memory systems known as systems consolidation. Previous work has suggested learning rules by which consolidation may…

Compared to the existing function-based models in deep generative modeling, the recently proposed diffusion models have achieved outstanding performance with a stochastic-process-based approach. But a long sampling time is required for this…