# Learn Feasibility Once, Optimize All Objectives: Derivative-Free Diffusion Models for Chance-Constrained Programming

arXiv: https://arxiv.org/abs/2610.03071 · HTML: https://mlsanity.com/paper/2610.03071/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 14 of its 39 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 14 of 14)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding](https://mlsanity.com/paper/2408.08252/) (2024)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Elements of Sequential Monte Carlo](https://mlsanity.com/paper/1903.04797/) (2019)
- [Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints](https://mlsanity.com/paper/2402.18012/) (2024)
- [DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Models](https://mlsanity.com/paper/2509.21655/) (2025)
- [Inference-Time Scaling of Discrete Diffusion Models via Importance Weighting and Optimal Proposal Design](https://mlsanity.com/paper/2505.22524/) (2025)
- [Lookahead Sample Reward Guidance for Test-Time Scaling of Diffusion Models](https://mlsanity.com/paper/2602.03211/) (2026)
- [A Proximal DC Algorithm for Sample Average Approximation of Chance Constrained Programming](https://mlsanity.com/paper/2301.00423/) (2023)
- [0/1 Constrained Optimization Solving Sample Average Approximation for Chance Constrained Programming](https://mlsanity.com/paper/2210.11889/) (2022)
- [A Gradient Guided Diffusion Framework for Chance Constrained Programming](https://mlsanity.com/paper/2510.12238/) (2025)

## Abstract (arXiv)

Chance-constrained programs (CCPs) optimize decisions under uncertainty by limiting the probability of constraint violation. Despite advances in traditional and learning-based approaches, optimizing non-convex or non-smooth objectives and adapting to different objectives under fixed chance constraints remain challenging. In this paper, we propose a Derivative-free Diffusion-based framework that Disentangles constraint modeling from objective optimization, termed D3Opt. We learn the chance-feasible structure once, independently of any particular objective, by training a risk-conditioned diffusion model solely on constraint-filtered decisions and freezing it as a reusable prior for post-specified objectives. At inference time, we propose an annealed, particle-based Feynman--Kac correction along the frozen reverse diffusion process to optimize post-specified objectives using only function evaluations. This enables derivative-free optimization of non-convex and non-smooth objectives without objective-specific retraining. We prove that the correction preserves feasibility when this property holds for the frozen prior, and derive an optimization-error bound separating learned-prior coverage, finite-particle approximation, and finite-temperature effects. Experiments on linear Gaussian CCPs, objective-transfer tasks, and chance-constrained economic dispatch demonstrate effective optimization across smooth and non-smooth objectives, including non-convex cases, and objective generalization under fixed chance constraints without retraining.