Related papers: Improved sampling via learned diffusions
This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing,…
We propose Image-to-Image Schr\"odinger Bridge (I$^2$SB), a new class of conditional diffusion models that directly learn the nonlinear diffusion processes between two given distributions. These diffusion bridges are particularly useful for…
Diffusion models have recently achieved remarkable success in generative modeling, yet their training dynamics across different noise levels remain highly imbalanced, which can lead to inefficient optimization and unstable learning…
The probabilistic diffusion model has become highly effective across various domains. Typically, sampling from a diffusion model involves using a denoising distribution characterized by a Gaussian with a learned mean and either fixed or…
Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…
We construct and analyze generative diffusions that transport a point mass to a prescribed target distribution over a finite time horizon using the stochastic interpolant framework. The drift is expressed as a conditional expectation that…
Diffusion-based classifiers such as those relying on the Personalized PageRank and the Heat kernel, enjoy remarkable classification accuracy at modest computational requirements. Their performance however is affected by the extent to which…
Diffusion models are a powerful class of generative models which simulate stochastic differential equations (SDEs) to generate data from noise. While diffusion models have achieved remarkable progress, they have limitations in unpaired…
We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. This imperfect communication poses a fundamental…
We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or…
Model-based reinforcement learning methods often use learning only for the purpose of estimating an approximate dynamics model, offloading the rest of the decision-making work to classical trajectory optimizers. While conceptually simple,…
This paper proposes a generative speech enhancement model based on Schr\"odinger bridge (SB). The proposed model is employing a tractable SB to formulate a data-to-data process between the clean speech distribution and the observed noisy…
Connecting optimal transport and variational inference, we present a principled and systematic framework for sampling and generative modelling centred around divergences on path space. Our work culminates in the development of the…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
Modern methods of generative modelling and unpaired data translation based on Schr\"odinger bridges and stochastic optimal control theory aim to transform an initial density to a target one in an optimal way. In the present paper, we assume…
Score-based diffusion models are frequently employed as structural priors in inverse problems. However, their iterative denoising process, initiated from Gaussian noise, often results in slow inference speeds. The Image-to-Image…
Training a diffusion model approximates a map from a data distribution $\rho$ to the optimal score function $s_t$ for that distribution. Can we differentiate this map? If we could, then we could predict how the score, and ultimately the…
We characterize the Schr\"odinger bridge problems by a family of Mckean-Vlasov stochastic control problems with no terminal time distribution constraint. In doing so, we use the theory of Hilbert space embeddings of probability measures and…
We consider the problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. Such settings have recently drawn considerable interest in the context of generative modelling…
Diffusion models are state-of-the-art methods in generative modeling when samples from a target probability distribution are available, and can be efficiently sampled, using score matching to estimate score vectors guiding a Langevin…