Constrained Generative Modeling with Manually Bridged Diffusion Models

• URL: http://arxiv.org/abs/2502.20371v1
• Date: Thu, 27 Feb 2025 18:41:46 GMT
• Title: Constrained Generative Modeling with Manually Bridged Diffusion Models
• Abstract summary: We introduce manual bridges, a framework that expands the kinds of constraints that can be practically used to form so-called diffusion bridges.<n>We develop a mechanism for combining multiple such constraints so that the resulting multiply-constrained model remains a manual bridge that respects all constraints.<n>We also develop a mechanism for training a diffusion model that respects such multiple constraints while also adapting it to match a data distribution.
• Score: 13.484619687662793
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper we describe a novel framework for diffusion-based generative modeling on constrained spaces. In particular, we introduce manual bridges, a framework that expands the kinds of constraints that can be practically used to form so-called diffusion bridges. We develop a mechanism for combining multiple such constraints so that the resulting multiply-constrained model remains a manual bridge that respects all constraints. We also develop a mechanism for training a diffusion model that respects such multiple constraints while also adapting it to match a data distribution. We develop and extend theory demonstrating the mathematical validity of our mechanisms. Additionally, we demonstrate our mechanism in constrained generative modeling tasks, highlighting a particular high-value application in modeling trajectory initializations for path planning and control in autonomous vehicles.

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