Related papers: Diffusion Schr\"{o}dinger Bridges for Bayesian Com…

Deep Gaussian processes (DGPs) enable expressive hierarchical Bayesian modeling but pose substantial challenges for posterior inference, especially over inducing variables. Denoising diffusion variational inference (DDVI) addresses this by…

Discrete Diffusion and Flow Matching models have significantly advanced generative modeling for discrete structures, including graphs. However, the dependencies between intermediate noisy states lead to error accumulation and propagation…

Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations…

Diffusion models have achieved remarkable success across a range of generative tasks. Recent efforts to enhance diffusion model architectures have reimagined them as a form of multi-task learning, where each task corresponds to a denoising…

Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…

In this work, we propose \texttt{TimeGrad}, an autoregressive model for multivariate probabilistic time series forecasting which samples from the data distribution at each time step by estimating its gradient. To this end, we use diffusion…

In text generation, models that generate text from scratch one token at a time are currently the dominant paradigm. Despite being performant, these models lack the ability to revise existing text, which limits their usability in many…

We propose to learn a generative model via entropy interpolation with a Schr\"{o}dinger Bridge. The generative learning task can be formulated as interpolating between a reference distribution and a target distribution based on the…

Offline planning often struggles with poor sampling efficiency as it tries to learn policies from scratch. Especially with diffusion models, such cold start practices mean that both training and sampling become very expensive. We…

Diffusion and flow-based models have enabled significant progress in generation tasks across various modalities and have recently found applications in predictive learning. However, unlike typical generation tasks that encourage sample…

Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant…

Diffusion models (DMs) as generative priors have recently shown great potential for denoising tasks but lack theoretical understanding with respect to their mean square error (MSE) optimality. This paper proposes a novel denoising strategy…

The denoising process of diffusion models can be interpreted as an approximate projection of noisy samples onto the data manifold. Moreover, the noise level in these samples approximates their distance to the underlying manifold. Building…

Source localization is the inverse problem of graph information dissemination and has broad practical applications. However, the inherent intricacy and uncertainty in information dissemination pose significant challenges, and the ill-posed…

We study generative modeling for time series using entropic optimal transport and the Schr\"odinger bridge (SB) framework, with a focus on applications in finance and energy modeling. Extending the diffusion-based approach of Hamdouche,…

Diffusion Probabilistic Models stand as a critical tool in generative modelling, enabling the generation of complex data distributions. This family of generative models yields record-breaking performance in tasks such as image synthesis,…

We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-Riemannian geometry, motivated by density control over…

In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion…

How diffusion models generalize beyond their training set is not known, and is somewhat mysterious given two facts: the optimum of the denoising score matching (DSM) objective usually used to train diffusion models is the score function of…

Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…