Arbitrarily-Conditioned Multi-Functional Diffusion for Multi-Physics Emulation

Da Long, Zhitong Xu, Guang Yang, Akil Narayan, Shandian Zhe
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:40270-40289, 2025.

Abstract

Modern physics simulation often involves multiple functions of interests, and traditional numerical approaches are known to be complex and computationally costly. While machine learning-based surrogate models can offer significant cost reductions, most focus on a single task, such as forward prediction, and typically lack uncertainty quantification — an essential component in many applications. To overcome these limitations, we propose Arbitrarily-Conditioned Multi-Functional Diffusion (ACM-FD), a versatile probabilistic surrogate model for multi-physics emulation. ACM-FD can perform a wide range of tasks within a single framework, including forward prediction, various inverse problems, and simulating data for entire systems or subsets of quantities conditioned on others. Specifically, we extend the standard Denoising Diffusion Probabilistic Model (DDPM) for multi-functional generation by modeling noise as Gaussian processes (GP). We propose a random-mask based, zero-regularized denoising loss to achieve flexible and robust conditional generation. We induce a Kronecker product structure in the GP covariance matrix, substantially reducing the computational cost and enabling efficient training and sampling. We demonstrate the effectiveness of ACM-FD across several fundamental multi-physics systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-long25b, title = {Arbitrarily-Conditioned Multi-Functional Diffusion for Multi-Physics Emulation}, author = {Long, Da and Xu, Zhitong and Yang, Guang and Narayan, Akil and Zhe, Shandian}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {40270--40289}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/long25b/long25b.pdf}, url = {https://proceedings.mlr.press/v267/long25b.html}, abstract = {Modern physics simulation often involves multiple functions of interests, and traditional numerical approaches are known to be complex and computationally costly. While machine learning-based surrogate models can offer significant cost reductions, most focus on a single task, such as forward prediction, and typically lack uncertainty quantification — an essential component in many applications. To overcome these limitations, we propose Arbitrarily-Conditioned Multi-Functional Diffusion (ACM-FD), a versatile probabilistic surrogate model for multi-physics emulation. ACM-FD can perform a wide range of tasks within a single framework, including forward prediction, various inverse problems, and simulating data for entire systems or subsets of quantities conditioned on others. Specifically, we extend the standard Denoising Diffusion Probabilistic Model (DDPM) for multi-functional generation by modeling noise as Gaussian processes (GP). We propose a random-mask based, zero-regularized denoising loss to achieve flexible and robust conditional generation. We induce a Kronecker product structure in the GP covariance matrix, substantially reducing the computational cost and enabling efficient training and sampling. We demonstrate the effectiveness of ACM-FD across several fundamental multi-physics systems.} }
Endnote
%0 Conference Paper %T Arbitrarily-Conditioned Multi-Functional Diffusion for Multi-Physics Emulation %A Da Long %A Zhitong Xu %A Guang Yang %A Akil Narayan %A Shandian Zhe %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-long25b %I PMLR %P 40270--40289 %U https://proceedings.mlr.press/v267/long25b.html %V 267 %X Modern physics simulation often involves multiple functions of interests, and traditional numerical approaches are known to be complex and computationally costly. While machine learning-based surrogate models can offer significant cost reductions, most focus on a single task, such as forward prediction, and typically lack uncertainty quantification — an essential component in many applications. To overcome these limitations, we propose Arbitrarily-Conditioned Multi-Functional Diffusion (ACM-FD), a versatile probabilistic surrogate model for multi-physics emulation. ACM-FD can perform a wide range of tasks within a single framework, including forward prediction, various inverse problems, and simulating data for entire systems or subsets of quantities conditioned on others. Specifically, we extend the standard Denoising Diffusion Probabilistic Model (DDPM) for multi-functional generation by modeling noise as Gaussian processes (GP). We propose a random-mask based, zero-regularized denoising loss to achieve flexible and robust conditional generation. We induce a Kronecker product structure in the GP covariance matrix, substantially reducing the computational cost and enabling efficient training and sampling. We demonstrate the effectiveness of ACM-FD across several fundamental multi-physics systems.
APA
Long, D., Xu, Z., Yang, G., Narayan, A. & Zhe, S.. (2025). Arbitrarily-Conditioned Multi-Functional Diffusion for Multi-Physics Emulation. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:40270-40289 Available from https://proceedings.mlr.press/v267/long25b.html.

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