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independent coupling

An independent coupling is a joint probability distribution over two or more random variables whose marginal distributions are specified and in which the variables are statistically independent of each other. Formed mathematically as the direct product measure of the individual marginals, it represents the default joint distribution where knowledge of one variable provides no information about the other. In probability theory, optimal transport, and continuous-time generative modeling frameworks like flows and diffusions, an independent coupling pairs samples from a source or base distribution with samples from a target distribution completely at random. This baseline formulation stands in contrast to dependent or optimal couplings, where sample pairs are explicitly correlated through conditioning, shared features, or cost-minimizing transport maps to guide the transformation between the underlying densities.

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Stochastic Interpolants with Data-Dependent Couplings

Stochastic Interpolants with Data-Dependent Couplings

Michael S. Albergo, Mark Goldstein, Nicholas Matthew Boffi, Rajesh Ranganath, Eric Vanden-Eijnden

Why you should read this

Proposes a framework for building continuous-time generative models by coupling base and target distributions conditioned on data, enabling efficient simulation-free training for conditional image super-resolution and in-painting tasks.

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 couple the base and the target densities, whereby samples from the base are computed conditionally given samples from the target in a way that is different from (but does not preclude) incorporating information about class labels or continuous embeddings. This enables us 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. The code is available at https://github.com/interpolants/couplings.

Added

2026-10-02