Infinite-dimensional Diffusion Bridge Simulation via Operator Learning
The diffusion bridge, which is a diffusion process conditioned on hitting a specific state within a finite period, has found broad applications in various scientific and engineering fields. However, simulating diffusion bridges for modeling natural data can be challenging due to both the intractability of the drift term and continuous representations of the data. Although several methods are available to simulate finite-dimensional diffusion bridges, infinite-dimensional cases remain under explored. This paper presents a method that merges score matching techniques with operator learning, enabling a direct approach to learn the infinite-dimensional bridge and achieving a discretization equivariant bridge simulation. We conduct a series of experiments, ranging from synthetic examples with closed-form solutions to the stochastic nonlinear evolution of real-world biological shape data. Our method demonstrates high efficacy, particularly due to its ability to adapt to any resolution without extra training.
Code (1)
Tasks
Bayesian InferenceOperator learningMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Stochastic Optimal Control for Diffusion Bridges in Function Spaces
Recent advancements in diffusion models and diffusion bridges primarily focus on finite-dimensional spaces, yet many real-world problems necessitate operations in infinite-dimensional function spaces for more natural and…
Image-to-Image TranslationTime SeriesMultilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generation
Score-based diffusion models (SBDM) have recently emerged as state-of-the-art approaches for image generation. Existing SBDMs are typically formulated in a finite-dimensional setting, where images are considered as tenso…
Image Generation$\infty$-Diff: Infinite Resolution Diffusion with Subsampled Mollified States
This paper introduces $\infty$-Diff, a generative diffusion model defined in an infinite-dimensional Hilbert space, which can model infinite resolution data. By training on randomly sampled subsets of coordinates and den…
DenoisingInfinite-Dimensional Diffusion Models
Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and th…
Time SeriesSymplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems
The modeling and simulation of infinite-dimensional Hamiltonian systems are central problems in mathematical physics and engineering, however they pose significant computational and structural challenges for standard dat…