The paper introduces Primal-Dual Flow Matching (PDFM), a method for learning data generators that satisfy user‑specified sample‑wise constraints with a guaranteed probability of satisfaction. PDFM builds on a population‑level constrained negative log‑likelihood objective and a flow‑matching parameterization, providing theoretical guarantees under regularity and expressivity assumptions. Practically, PDFM requires only binary membership oracle feedback, avoids differentiable distance metrics or convexity assumptions, and empirically outperforms vanilla flow matching while maintaining distributional fidelity.
arXiv:2610.02260v1 Announce Type: new Abstract: Flow matching models excel at generative modeling, and many downstream applications require their samples to satisfy prescribed constraints, such as ob...
arXiv:2607. 04513v1 Announce Type: cross Abstract: Flow matching is a powerful tool for generative modeling, but emerging applications in robotics, planning, and physics require inference-time constraints on generated outputs.
arXiv:2607. 14424v1 Announce Type: cross Abstract: In recent years Flow Matching has become a prominent method for generative modeling robot motion generation.
arXiv:2606. 13400v1 Announce Type: cross Abstract: While flow-based generative models have demonstrated strong performance across a wide range of domains, deploying them in safety-critical physical systems remains challenging due to strict constraint requirements.
Flow matching is a powerful tool for generative modeling, but emerging applications in robotics, planning, and physics require inference-time constraints on generated outputs. Such constraints are often complex and highly nonlinear.
arXiv:2602. 21429v3 Announce Type: replace Abstract: Flow-based generative models, such as diffusion models and flow matching models, have achieved remarkable success in learning complex data distributions.
The paper introduces ORACLE, a method for constrained learning that evaluates constraint compatibility after the optimizer has taken a step, rather than before. ORACLE performs a joint endpoint linearization of diverse constraint families, constructs an alignment in the optimizer’s geometry, bounds its authority, and commits the adjustment only after validation. Experiments on eight PDE benchmarks with four different optimizers show that ORACLE matches or improves performance in 94% of configurations, outperforming other constraint-handling approaches.
arXiv:2606. 04816v1 Announce Type: new Abstract: Large language models (LLMs) increasingly translate natural-language optimization problems into executable solver code.
The paper introduces Function Projection for Flow Matching (FP‑FM), an algorithm that conditions generative models directly on samples from a target distribution. FP‑FM learns basis functions spanning velocity fields for training distributions and adapts to new distributions via a simple least‑squares projection, enabling efficient sample generation without additional training at inference time. Variants of the method trade expressivity for computational cost by enriching coefficient calculations, and the approach shows markedly better precision and recall than baselines, especially on unseen distributions.
CG4AI is a column generation framework that trains AI models while enforcing linear constraints on their outputs. It constructs a convex combination of models, using a master linear program to set mixture weights and a pricing subproblem to generate new models guided by dual variables, focusing on the most violated constraints. The method is applied to MNIST digit classification—demonstrating constraint learning, adversarial robustness, error correction, and output relabeling—and to multi‑commodity flow routing, achieving feasible predictors with higher accuracy than single‑model baselines.
ParetoTransport is a training‑free guidance method for pre‑trained flow‑matching models that explicitly refines a population‑level distribution in objective space. It iteratively transports the empirical offline distribution toward the Pareto front using Wasserstein matching to intermediate proxy distributions, thereby controlling distributional displacement and mass allocation along the front. The authors prove a convergence result and show state‑of‑the‑art performance on standard offline multi‑objective optimization benchmarks, evaluating beyond hypervolume to generational distance, inverted generational distance, and Wasserstein distance.
arXiv:2607. 23480v1 Announce Type: new Abstract: Variational autoencoders (VAEs) transform high-dimensional, often noisy data into a compact latent representation, making downstream optimization more tractable.