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Constrained Synthesis with Projected Diffusion Models
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This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative diffusion models as a constrained optimization problem, steering the generated data distribution to remain within a specified region to ensure adherence to the given constraints. These capabilities are validated on applications featuring both convex and challenging, non-convex, constraints as well as ordinary differential equations, in domains spanning from synthesizing new materials with precise morphometric properties, generating physics-informed motion, optimizing paths in planning scenarios, and human motion synthesis.
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Cited by 3 Pith papers
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Should the Boundary Term Be Learned in Reflected Diffusion? Conormal Trace and Reflection Masking
For reflected diffusion on bounded domains, the no-flux condition fixes one scalar per boundary point, the conormal trace of the score, and the paper gives an exact box parametrization, proves a misspecification floor...
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Integration Matters: Rollout-Based Training for Constrained Diffusion Models
Rollout-based fine-tuning with a learned adaptive guidance scaling yields near-zero constraint violations while preserving sample fidelity in constrained diffusion models.
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Physics-Informed Diffusion Models for Unsupervised Anomaly Detection in Multivariate Time Series
A weighted physics-informed loss schedule during diffusion training improves unsupervised anomaly detection in multivariate time series, according to the paper's experiments.
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