Graphically Structured Diffusion Models

Christian Dietrich Weilbach, William Harvey, Frank Wood
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:36887-36909, 2023.

Abstract

We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model’s performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-weilbach23a, title = {Graphically Structured Diffusion Models}, author = {Weilbach, Christian Dietrich and Harvey, William and Wood, Frank}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {36887--36909}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/weilbach23a/weilbach23a.pdf}, url = {https://proceedings.mlr.press/v202/weilbach23a.html}, abstract = {We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model’s performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.} }
Endnote
%0 Conference Paper %T Graphically Structured Diffusion Models %A Christian Dietrich Weilbach %A William Harvey %A Frank Wood %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-weilbach23a %I PMLR %P 36887--36909 %U https://proceedings.mlr.press/v202/weilbach23a.html %V 202 %X We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model’s performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.
APA
Weilbach, C.D., Harvey, W. & Wood, F.. (2023). Graphically Structured Diffusion Models. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:36887-36909 Available from https://proceedings.mlr.press/v202/weilbach23a.html.

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