# Support-Proximity Augmented Diffusion Estimation for Offline Black-Box Optimization

arXiv: https://arxiv.org/abs/2605.11246 · HTML: https://mlsanity.com/paper/2605.11246/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 44 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 30 of 34)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [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)
- [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)
- [Diffusion Models for Black-Box Optimization](https://mlsanity.com/paper/2306.07180/) (2023)
- [ROBEL: Robotics Benchmarks for Learning with Low-Cost Robots](https://mlsanity.com/paper/1909.11639/) (2019)
- [The reparameterization trick for acquisition functions](https://mlsanity.com/paper/1712.00424/) (2017)
- [Feedback Efficient Online Fine-Tuning of Diffusion Models](https://mlsanity.com/paper/2402.16359/) (2024)
- [Autofocused oracles for model-based design](https://mlsanity.com/paper/2006.08052/) (2020)
- [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)
- [Bidirectional Learning for Offline Infinite-width Model-based Optimization](https://mlsanity.com/paper/2209.07507/) (2022)
- [OmniPred: Language Models as Universal Regressors](https://mlsanity.com/paper/2402.14547/) (2024)
- [Importance-aware Co-teaching for Offline Model-based Optimization](https://mlsanity.com/paper/2309.11600/) (2023)
- [Parallel-mentoring for Offline Model-based Optimization](https://mlsanity.com/paper/2309.11592/) (2023)
- [Offline Model-Based Optimization via Policy-Guided Gradient Search](https://mlsanity.com/paper/2405.05349/) (2024)
- [ParetoFlow: Guided Flows in Multi-Objective Optimization](https://mlsanity.com/paper/2412.03718/) (2024)
- [Guided Trajectory Generation with Diffusion Models for Offline Model-based Optimization](https://mlsanity.com/paper/2407.01624/) (2024)
- [Offline Model-Based Optimization: Comprehensive Review](https://mlsanity.com/paper/2503.17286/) (2025)
- [Offline Model-Based Optimization by Learning to Rank](https://mlsanity.com/paper/2410.11502/) (2024)
- [Generative Adversarial Model-Based Optimization via Source Critic Regularization](https://mlsanity.com/paper/2402.06532/) (2024)
- [Design Editing for Offline Model-based Optimization](https://mlsanity.com/paper/2405.13964/) (2024)

## Built on by (most cited first, 1 of 1)

- [One Sentence, One Drama: Personalized Short-Form Drama Generation via Multi-Agent Systems](https://mlsanity.com/paper/2605.22144/) (2026)

## Abstract (arXiv)

Offline black-box optimization aims to discover novel designs with high property scores using only a static dataset, a task fundamentally challenged by the out-of-distribution (OOD) extrapolation problem. Existing approaches typically bifurcate into inverse methods, which struggle with the ill-posed nature of mapping scores to designs, and forward methods, which often lack the distributional expressivity to quantify uncertainty effectively. In this work, we propose SPADE (Support-Proximity Augmented Diffusion Estimation), a novel framework that reimagines forward surrogate modeling through the lens of conditional generative modeling. SPADE models the forward likelihood p(y|x) using a diffusion model, but with two critical enhancements to tailor it for optimization: (1) a Calibrated Diffusion Estimation module that enforces global consistency in statistical moments and pairwise rankings, and (2) a Support-Proximity Regularization mechanism that implicitly internalizes the data manifold constraint p(x) via kNN-based density estimation. Theoretically, we prove that our regularization is first-order equivalent to maximizing a Bayesian posterior with a valid design prior. Empirically, SPADE achieves state-of-the-art performance across Design-Bench tasks and an LLM data mixture optimization benchmark.