Gradient-Free Generation for Hard-Constrained Systems

ICLR 2025 Conference Submission1656 Authors

Keywords: Flow Matching, Generative Model, Constrained Generation, Partial Differential Equations, Conservation Laws

TL;DR: We propose ECI sampling, a gradient-free approach for guiding pre-trained generative models for hard-constrained generation.

Abstract: Generative models that satisfy hard constraints are crucial in scientific applications, e.g., numerical simulations, dynamical systems, and supply chain optimization, where physical laws or system requirements must be strictly respected. However, many existing constrained generative models, especially those developed for computer vision, rely heavily on gradient information, which is often sparse or computationally expensive in other fields, e.g., partial differential equations (PDEs). Accurately solving these problems numerically demands the generated solutions to comply with strict physical constraints, e.g., conservation laws. In this work, we introduce a novel framework for adapting pre-trained, unconstrained generative models to exactly satisfy constraints in a zero-shot manner, without requiring expensive gradient computations or fine-tuning. Our framework, ECI sampling, alternates between extrapolation (E), correction (C), and interpolation (I) stages during each iterative sampling step to ensure accurate integration of constraint information while preserving the validity of the generated outputs. We demonstrate the efficacy of our approach across various PDE systems, showing that ECI-guided generation strictly adheres to physical constraints and accurately captures complex distribution shifts induced by these constraints. Empirical results show that our framework consistently outperforms baseline approaches in both zero-shot constrained generative and regression tasks, and achieves competitive results without additional fine-tuning.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 1656