Chance-constrained Flow Matching for High-Fidelity Constraint-aware Generation
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918150799360000 |
|---|---|
| author | Liang, Jinhao Sun, Yixuan Samaddar, Anirban Madireddy, Sandeep Fioretto, Ferdinando |
| author_facet | Liang, Jinhao Sun, Yixuan Samaddar, Anirban Madireddy, Sandeep Fioretto, Ferdinando |
| contents | Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples onto the feasible set; however, repeated projection can distort the learned distribution and induce a mismatch with the data manifold. Thus, recent multi-stage procedures attempt to defer projection to clean samples during sampling, but they increase algorithmic complexity and accumulate errors across steps. This paper addresses these challenges by proposing a novel training-free method, Chance-constrained Flow Matching (CCFM), that integrates stochastic optimization into the sampling process, enabling effective enforcement of hard constraints while maintaining high-fidelity sample generation. Importantly, CCFM guarantees feasibility in the same manner as conventional repeated projection, yet, despite operating directly on noisy intermediate samples, it is theoretically equivalent to projecting onto the feasible set defined by clean samples. This yields a sampler that mitigates distributional distortion. Empirical experiments show that CCFM outperforms current state-of-the-art constrained generative models in modeling complex physical systems governed by partial differential equations and molecular docking problems, delivering higher feasibility and fidelity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25157 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chance-constrained Flow Matching for High-Fidelity Constraint-aware Generation Liang, Jinhao Sun, Yixuan Samaddar, Anirban Madireddy, Sandeep Fioretto, Ferdinando Machine Learning Artificial Intelligence Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples onto the feasible set; however, repeated projection can distort the learned distribution and induce a mismatch with the data manifold. Thus, recent multi-stage procedures attempt to defer projection to clean samples during sampling, but they increase algorithmic complexity and accumulate errors across steps. This paper addresses these challenges by proposing a novel training-free method, Chance-constrained Flow Matching (CCFM), that integrates stochastic optimization into the sampling process, enabling effective enforcement of hard constraints while maintaining high-fidelity sample generation. Importantly, CCFM guarantees feasibility in the same manner as conventional repeated projection, yet, despite operating directly on noisy intermediate samples, it is theoretically equivalent to projecting onto the feasible set defined by clean samples. This yields a sampler that mitigates distributional distortion. Empirical experiments show that CCFM outperforms current state-of-the-art constrained generative models in modeling complex physical systems governed by partial differential equations and molecular docking problems, delivering higher feasibility and fidelity. |
| title | Chance-constrained Flow Matching for High-Fidelity Constraint-aware Generation |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2509.25157 |