Related papers: Mirror Bridges Between Probability Measures

Diffusion models often yield highly curved trajectories and noisy score targets due to an uninformative, memoryless forward process that induces independent data-noise coupling. We propose Adjoint Schr\"odinger Bridge Matching (ASBM), a…

We study stochastic density control between Gaussian-mixture endpoint distributions under Brownian prior dynamics. Since the direct Schr\"odinger bridge between Gaussian mixtures is generally not available in closed form, we introduce a…

Diffusion bridge models offer a powerful framework for connecting two data distributions, such as in image restoration and translation. Many existing methods learn this bridge by mimicking the score-matching formulation of standard…

In some applied scenarios, the availability of complete data is restricted, often due to privacy concerns; only aggregated, robust and inefficient statistics derived from the data are made accessible. These robust statistics are not…

The purpose of the present work is to expand substantially the type of control and estimation problems that can be addressed following the paradigm of Schr\"odinger bridges, by incorporating termination (killing) of stochastic flows.…

Given an unconditional diffusion model targeting a joint model $\pi(x, y)$, using it to perform conditional simulation $\pi(x \mid y)$ is still largely an open question and is typically achieved by learning conditional drifts to the…

A learning classifier must outperform a trivial solution, in case of imbalanced data, this condition usually does not hold true. To overcome this problem, we propose a novel data level resampling method - Clustering Based Oversampling for…

Sampling from high-dimensional distributions is a fundamental problem in statistical research and practice. However, great challenges emerge when the target density function is unnormalized and contains isolated modes. We tackle this…

Retrosynthesis planning is a fundamental challenge in chemistry which aims at designing reaction pathways from commercially available starting materials to a target molecule. Each step in multi-step retrosynthesis planning requires accurate…

The solution of the path structured multimarginal Schr\"{o}dinger bridge problem (MSBP) is the most-likely measure-valued trajectory consistent with a sequence of observed probability measures or distributional snapshots. We leverage recent…

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion…

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…

Motivated by applications in trajectory inference and particle tracking, we introduce Smooth Schr\"odinger Bridges. Our proposal generalizes prior work by allowing the reference process in the Schr\"odinger Bridge problem to be a smooth…

Many problems in computational science and engineering become one-to-many after coarse graining, partial observation, or inverse reconstruction: a resolved state may not determine a unique subgrid forcing, a structural descriptor may not…

Scientists often want to make predictions beyond the observed time horizon of "snapshot" data following latent stochastic dynamics. For example, in time course single-cell mRNA profiling, scientists have access to cellular transcriptional…

Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…

Transporting between arbitrary distributions is a fundamental goal in generative modeling. Recently proposed diffusion bridge models provide a potential solution, but they rely on a joint distribution that is difficult to obtain in…

The estimation of mutual information (MI) or conditional mutual information (CMI) from a set of samples is a long-standing problem. A recent line of work in this area has leveraged the approximation power of artificial neural networks and…

The reconstruction of physical fields from sparse measurements is pivotal in both scientific research and engineering applications. Traditional methods are increasingly supplemented by deep learning models due to their efficacy in…

For a fixed flow-based generative model under a small inference budget, sample quality can depend strongly on where the sampler spends its few function evaluations. Flow matching and Schr\"odinger bridges define probability paths, yet their…