# Generative Refinement for Low-Budget Black-Box Optimization

arXiv: https://arxiv.org/abs/2607.00691 · HTML: https://mlsanity.com/paper/2607.00691/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 48 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Conditioning by adaptive sampling for robust design](https://mlsanity.com/paper/1901.10060/) (2019)
- [Design-Bench: Benchmarks for Data-Driven Offline Model-Based Optimization](https://mlsanity.com/paper/2202.08450/) (2022)
- [Test-time Alignment of Diffusion Models without Reward Over-optimization](https://mlsanity.com/paper/2501.05803/) (2025)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [Conservative Objective Models for Effective Offline Model-Based Optimization](https://mlsanity.com/paper/2107.06882/) (2021)
- [Model Inversion Networks for Model-Based Optimization](https://mlsanity.com/paper/1912.13464/) (2019)
- [Bayesian optimization for materials design](https://mlsanity.com/paper/1506.01349/) (2015)
- [Diffusion Models for Black-Box Optimization](https://mlsanity.com/paper/2306.07180/) (2023)
- [Inference-Time Alignment of Diffusion Models with Direct Noise Optimization](https://mlsanity.com/paper/2405.18881/) (2024)
- [RoMA: Robust Model Adaptation for Offline Model-based Optimization](https://mlsanity.com/paper/2110.14188/) (2021)
- [Generative Pretraining for Black-Box Optimization](https://mlsanity.com/paper/2206.10786/) (2022)
- [Data-Driven Offline Decision-Making via Invariant Representation Learning](https://mlsanity.com/paper/2211.11349/) (2022)
- [Reward-Guided Iterative Refinement in Diffusion Models at Test-Time with Applications to Protein and DNA Design](https://mlsanity.com/paper/2502.14944/) (2025)
- [Bidirectional Learning for Offline Model-based Biological Sequence Design](https://mlsanity.com/paper/2301.02931/) (2023)
- [Posterior Inference with Diffusion Models for High-dimensional Black-box Optimization](https://mlsanity.com/paper/2502.16824/) (2025)
- [Design Editing for Offline Model-based Optimization](https://mlsanity.com/paper/2405.13964/) (2024)
- [Robust Guided Diffusion for Offline Black-Box Optimization](https://mlsanity.com/paper/2410.00983/) (2024)
- [Fast Direct: Query-Efficient Online Black-box Guidance for Diffusion-model Target Generation](https://mlsanity.com/paper/2502.01692/) (2025)
- [Investigating Bayesian optimization for expensive-to-evaluate black box functions: Application in fluid dynamics](https://mlsanity.com/paper/2207.09154/) (2022)
- [Diffusion-BBO: Diffusion-Based Inverse Modeling for Online Black-Box Optimization](https://mlsanity.com/paper/2407.00610/) (2024)
- [A Principled Approach to Design Using High Fidelity Fluid-Structure Interaction Simulations](https://mlsanity.com/paper/2008.09687/) (2020)

## Abstract (arXiv)

Black-box optimization is a fundamental tool in science and engineering for optimizing objectives when gradient information is unavailable. It becomes especially difficult when the objective function is expensive to evaluate, limiting the evaluation budget to a few tens or hundreds of queries, and when good solutions occupy complex, low-measure regions of the search space. Generative models can supply useful structural priors in such settings, but existing generative BBO approaches bring significant evaluation cost. We identify three design principles for generative optimization under such low-budget conditions: avoid objective learning, optimize in candidate space, and make every evaluation count. Together, these principles motivate separating structural modeling from objective-driven search. We instantiate them in SPARROW, a simple sequential optimizer that maintains a persistent, ranked archive of evaluated candidates and uses a fixed, unconditional generative sampler solely as a corruption-refinement operator. SPARROW requires only access to the sampler's corruption and refinement processes, and never needs to evaluate the objective to train or guide it. Across three complementary settings, probing thin feasible geometry, disconnected high-performing regions, and failure-prone evaluations, SPARROW outperforms classical and generative baselines under strict evaluation budgets. These results demonstrate that separating structural priors from objective-driven search can be effective when evaluations are scarce and the search geometry is challenging.