# D-IMPL: A Diffusion-based Solver for Parameterized BBOs

arXiv: https://arxiv.org/abs/2609.22752 · HTML: https://mlsanity.com/paper/2609.22752/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 20 of its 26 references that are in the map.
- First posted on arXiv 19 Sep 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
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- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoisers](https://mlsanity.com/paper/2211.01324/) (2022)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Tutorial on amortized optimization](https://mlsanity.com/paper/2202.00665/) (2022)
- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [Diffusion Models for Black-Box Optimization](https://mlsanity.com/paper/2306.07180/) (2023)
- [Diffusion Model Predictive Control](https://mlsanity.com/paper/2410.05364/) (2024)
- [Diffusion Predictive Control with Constraints](https://mlsanity.com/paper/2412.09342/) (2024)
- [Diffusion Model for Data-Driven Black-Box Optimization](https://mlsanity.com/paper/2403.13219/) (2024)
- [Improve Single-Point Zeroth-Order Optimization Using High-Pass and Low-Pass Filters](https://mlsanity.com/paper/2111.01701/) (2021)
- [Toward Near-Globally Optimal Nonlinear Model Predictive Control via Diffusion Models](https://mlsanity.com/paper/2412.08278/) (2024)
- [Escaping saddle points in zeroth-order optimization: the power of two-point estimators](https://mlsanity.com/paper/2209.13555/) (2022)
- [TS-RSR: A provably efficient approach for batch Bayesian Optimization](https://mlsanity.com/paper/2403.04764/) (2024)
- [Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access](https://mlsanity.com/paper/2505.18344/) (2025)
- [DiffOPF: Diffusion Solver for Optimal Power Flow](https://mlsanity.com/paper/2510.14075/) (2025)

## Abstract (arXiv)

Diffusion models have demonstrated strong power in generative modeling tasks across multiple domains, exhibiting a remarkable capability of learning complex distributions from samples. In this paper, we leverage such capability to design an efficient universal diffusion-based solver for parameterized black-box optimizations (BBO), where the optimizer has only black-box access to queries of the objective function at the learning stage, yet is able to reduce the additional computational cost at the inference stage for each BBO instance while also capturing the potential multi-modal landscape of non-convex objectives. To cast our formulation as a compatible generative modeling task, we introduce the notion of minimization policy as a new solution concept, which defines a sampling distribution over the solutions that should concentrate around the minimizer set for each BBO instance. We then propose Diffusion-based Iterative Minimization Policy Learning (D-IMPL), a practical generative-model-based solver for solving parameterized BBOs that employs diffusion models to learn a minimization policy, whose density is proportional to the exponential of the negated objective values, thereby amortizing the computational costs across different BBO instances. Furthermore, we demonstrate the performance of our D-IMPL algorithm by establishing a sample complexity guarantee showing that a δ-approximate minimization policy can be effectively learned within O(log(1/δ)) iterations, and by extensive empirical evaluations over a range of constrained and unconstrained BBO tasks.