Related papers: Adjoint Schr\"odinger Bridge Sampler
Sampling from a distribution $p(x) \propto e^{-\mathcal{E}(x)}$ known up to a normalising constant is an important and challenging problem in statistics. Recent years have seen the rise of a new family of amortised sampling algorithms,…
The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certain transportation cost. This problem, which represents a generalisation of optimal transport…
Generative diffusion models use time-forward and backward stochastic differential equations to connect the data and prior distributions. While conventional diffusion models (e.g., score-based models) only learn the backward process, more…
Score-based generative models have recently attracted significant attention for their ability to generate high-fidelity data by learning maps from simple Gaussian priors to complex data distributions. A natural generalization of this idea…
Learning-based methods for sampling from the Gibbs distribution in finite-dimensional spaces have progressed quickly, yet theory and algorithmic design for infinite-dimensional function spaces remain limited. This gap persists despite their…
The dynamic Schr\"odinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a…
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…
We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…
Coordinated multi-arm manipulation requires satisfying multiple simultaneous geometric constraints across high-dimensional configuration spaces, which poses a significant challenge for traditional planning and control methods. In this work,…
At the core of modern generative modeling frameworks, including diffusion models, score-based models, and flow matching, is the task of transforming a simple prior distribution into a complex target distribution through stochastic paths in…
Understanding complex systems by inferring trajectories from sparse sample snapshots is a fundamental challenge in a wide range of domains, e.g., single-cell biology, meteorology, and economics. Despite advancements in Bridge and Flow…
Metasurface inverse design is challenged by the intricate relationship between structural parameters and electromagnetic responses, as well as the high dimensionality of the optimization space. Local models, while commonly employed, quickly…
Deep Ensemble (DE) approach is a straightforward technique used to enhance the performance of deep neural networks by training them from different initial points, converging towards various local optima. However, a limitation of this…
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…
The momentum Schr\"odinger Bridge (mSB) has emerged as a leading method for accelerating generative diffusion processes and reducing transport costs. However, the lack of simulation-free properties inevitably results in high training costs…
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,…
Boltzmann machines (BMs) are powerful energy-based generative models, but their heavy training cost has largely confined practical use to Restricted BMs (RBMs) trained with an efficient learning method called contrastive divergence. More…
Image inpainting is an important image generation task, which aims to restore corrupted image from partial visible area. Recently, diffusion Schr\"odinger bridge methods effectively tackle this task by modeling the translation between…
Scalable sampling of molecular states in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann generators tackle this problem by pairing normalizing flows with importance sampling to obtain uncorrelated…
Diffusion models serve as a powerful generative framework for solving inverse problems. However, they still face two key challenges: 1) the distortion-perception tradeoff, where improving perceptual quality often degrades reconstruction…