Stochastic interpolants with data-dependent couplings
Primary Area: generative models
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Keywords: flows, diffusions, stochastic interpolants, generative models, sde, ode, image generation
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TL;DR: Building generative models by coupling data and base distributions using stochastic interpolants.
Abstract: Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to \textit{couple} the base and the target densities. This enables us to incorporate information about class labels or continuous embeddings such as textual representations to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting, where we show that the use of a data-informed base density incorporating information about partially masked or low-resolution images significantly improves performance.
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Submission Number: 9016
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