# In-Context Batch Black-box Optimization via Flow Matching

arXiv: https://arxiv.org/abs/2610.20138 · HTML: https://mlsanity.com/paper/2610.20138/

## 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 25 of its 37 references that are in the map.
- First posted on arXiv 14 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, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [Batch Bayesian Optimization via Local Penalization](https://mlsanity.com/paper/1505.08052/) (2015)
- [Reflected Diffusion Models](https://mlsanity.com/paper/2304.04740/) (2023)
- [HEBO Pushing The Limits of Sample-Efficient Hyperparameter Optimisation](https://mlsanity.com/paper/2012.03826/) (2020)
- [PFNs4BO: In-Context Learning for Bayesian Optimization](https://mlsanity.com/paper/2305.17535/) (2023)
- [A Langevin-like Sampler for Discrete Distributions](https://mlsanity.com/paper/2206.09914/) (2022)
- [End-to-End Meta-Bayesian Optimisation with Transformer Neural Processes](https://mlsanity.com/paper/2305.15930/) (2023)
- [Langevin Monte Carlo without smoothness](https://mlsanity.com/paper/1905.13285/) (2019)
- [Reinforced Few-Shot Acquisition Function Learning for Bayesian Optimization](https://mlsanity.com/paper/2106.04335/) (2021)
- [Amortized Probabilistic Conditioning for Optimization, Simulation and Inference](https://mlsanity.com/paper/2410.15320/) (2024)
- [Gaussian Mixture Flow Matching Models](https://mlsanity.com/paper/2504.05304/) (2025)
- [Posterior Inference with Diffusion Models for High-dimensional Black-box Optimization](https://mlsanity.com/paper/2502.16824/) (2025)
- [BOFormer: Learning to Solve Multi-Objective Bayesian Optimization via Non-Markovian RL](https://mlsanity.com/paper/2505.21974/) (2025)
- [PABBO: Preferential Amortized Black-Box Optimization](https://mlsanity.com/paper/2503.00924/) (2025)
- [MONGOOSE: Path-wise Smooth Bayesian Optimisation via Meta-learning](https://mlsanity.com/paper/2302.11533/) (2023)
- [In-Context Multi-Objective Optimization](https://mlsanity.com/paper/2512.11114/) (2025)
- [Generative Bayesian Optimization: Generative Models as Acquisition Functions](https://mlsanity.com/paper/2510.25240/) (2025)
- [Batched Energy-Entropy acquisition for Bayesian Optimization](https://mlsanity.com/paper/2410.08804/) (2024)
- [In-Context Black-Box Optimization with Unreliable Feedback](https://mlsanity.com/paper/2605.06187/) (2026)
- [α-PFN: Fast Entropy Search via In-Context Learning](https://mlsanity.com/paper/2606.07134/) (2026)

## Abstract (arXiv)

Batch black-box optimization is important for expensive systems where many candidates can be evaluated in parallel, yet only a few rounds of evaluation are affordable. In this regime, effective batch construction must identify multiple promising regions while avoiding redundant evaluations, and conventional Bayesian optimization can require increasingly difficult batch-selection procedures as the batch size grows. We introduce Flow Matching for Thompson-Sampling Refinement (FMTR), an amortized approach that learns offline a continuous, history-conditioned proposal distribution from which variable-size batches can be sampled. FMTR is trained offline by conditional flow matching on Thompson-sampling argmaxes refined toward high-value regions via a horizon-dependent Langevin pushforward map, adapting the exploration-exploitation tradeoff over the optimization horizon. At test time, the model parameters remain fixed and batch generation requires neither task-specific surrogate refitting nor numerical acquisition optimization. FMTR achieves strong performance against batch BO and in-context baselines on synthetic and real-world benchmarks, while substantially reducing the computational cost of batch selection.