Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel

• URL: http://arxiv.org/abs/2310.03054v3
• Date: Thu, 21 Mar 2024 12:43:34 GMT
• Title: Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel
• Authors: Paul Hagemann, Johannes Hertrich, Fabian Altekrüger, Robert Beinert, Jannis Chemseddine, Gabriele Steidl,
• Abstract summary: conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. We approximate the joint distribution of the ground truth and the observations using discrete Wasserstein gradient flows.
• Score: 2.199065293049186
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. This MMD, which is also known as energy distance, has several advantageous properties like efficient computation via slicing and sorting. We approximate the joint distribution of the ground truth and the observations using discrete Wasserstein gradient flows and establish an error bound for the posterior distributions. Further, we prove that our particle flow is indeed a Wasserstein gradient flow of an appropriate functional. The power of our method is demonstrated by numerical examples including conditional image generation and inverse problems like superresolution, inpainting and computed tomography in low-dose and limited-angle settings.

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