Stochastic Interpolants with Data-Dependent Couplings

Michael Samuel Albergo, Mark Goldstein, Nicholas Matthew Boffi, Rajesh Ranganath, Eric Vanden-Eijnden
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:921-937, 2024.

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 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-albergo24a, title = {Stochastic Interpolants with Data-Dependent Couplings}, author = {Albergo, Michael Samuel and Goldstein, Mark and Boffi, Nicholas Matthew and Ranganath, Rajesh and Vanden-Eijnden, Eric}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {921--937}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/albergo24a/albergo24a.pdf}, url = {https://proceedings.mlr.press/v235/albergo24a.html}, 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 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.} }
Endnote
%0 Conference Paper %T Stochastic Interpolants with Data-Dependent Couplings %A Michael Samuel Albergo %A Mark Goldstein %A Nicholas Matthew Boffi %A Rajesh Ranganath %A Eric Vanden-Eijnden %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-albergo24a %I PMLR %P 921--937 %U https://proceedings.mlr.press/v235/albergo24a.html %V 235 %X 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.
APA
Albergo, M.S., Goldstein, M., Boffi, N.M., Ranganath, R. & Vanden-Eijnden, E.. (2024). Stochastic Interpolants with Data-Dependent Couplings. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:921-937 Available from https://proceedings.mlr.press/v235/albergo24a.html.

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