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Constrained Generative Modeling for Science and Engineering
Abstract:
Despite the remarkable generative capabilities of diffusion and flow matching models, their integration into safety-critical or scientifically rigorous applications remains hindered by the need to ensure compliance with stringent physical, structural, and operational constraints. The research conducted in preparation for this proposal has addressed this challenge through the integration of constrained optimization into the sampling process, enabling the generation of certifiably consistent samples under user-defined functional and logic constraints. This key feature is provided for both continuous and discrete diffusion models, enabling, for the first time, the generation of both continuous (e.g., images and trajectories) and discrete (e.g., molecular structures and natural language) outputs that strictly comply with constraints. However, while constrained sampling approaches pioneered during the first stage of this research show significant promise, distribution quality often degrades as compared to the unconstrained sampling approaches. This proposal argues that this performance trade-off stems from the misalignment between the training objective and the constrained sampling process.
State-of-the-art constrained generation methods rely on the integration of projections onto the feasible set during the sampling process, pushing the samples towards low density regions which may not have been learned during the training process. The outlined research addresses this disconnect by introducing an end-to-end training procedure, ensuring alignment between the training process and sampling.
Committee:
- Aidong Zhang, Committee Chair, CS, BME/SEAS, SDS/UVA
- Ferdinando Fioretto, Advisor, CS/SEAS/UVA
- Thomas Hartvigsen, SDS/UVA
- Stephen Baek, SDS/UVA
- Yu Meng, CS/SEAS/UVA