# Sample-Efficient Optimisation over the Outputs of Generative Models

arXiv: https://arxiv.org/abs/2509.23800 · HTML: https://mlsanity.com/paper/2509.23800/

## 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 43 of its 57 references that are in the map.
- First posted on arXiv 28 Sep 2025.

## Placed in

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

## Builds on (most cited first, 30 of 43)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [HunyuanVideo: A Systematic Framework For Large Video Generative Models](https://mlsanity.com/paper/2412.03603/) (2024)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [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)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [Stable Audio Open](https://mlsanity.com/paper/2407.14358/) (2024)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [Neural Architecture Optimization](https://mlsanity.com/paper/1808.07233/) (2018)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [Sample-Efficient Optimization in the Latent Space of Deep Generative Models via Weighted Retraining](https://mlsanity.com/paper/2006.09191/) (2020)
- [Local Latent Space Bayesian Optimization over Structured Inputs](https://mlsanity.com/paper/2201.11872/) (2022)
- [Diffusion Models for Black-Box Optimization](https://mlsanity.com/paper/2306.07180/) (2023)
- [High-Dimensional Bayesian Optimisation with Variational Autoencoders and Deep Metric Learning](https://mlsanity.com/paper/2106.03609/) (2021)
- [On Exact Inversion of DPM-Solvers](https://mlsanity.com/paper/2311.18387/) (2023)

## Abstract (arXiv)

Modern generative AI models, such as diffusion and flow matching models, can sample from rich data distributions. However, many applications, especially in science and engineering, require more than drawing samples from the model distribution: they require searching within this distribution for samples that optimise task-specific criteria. In this work, we propose O3 (Optimisation Over the Outputs of Generative Models), a method for sample-efficient black-box optimisation over continuous-variable diffusion and flow-matching models. O3 is built around surrogate latent spaces: low-dimensional Euclidean embeddings that can be extracted from a generative model without additional training. The resulting representations have controllable dimensionality and support the direct application of standard optimisation algorithms. We show, on image and protein design tasks, that surrogate-space optimisation finds substantially higher-scoring samples than standard sampling or optimisation in the original latent space. Our method is model- and optimiser-agnostic, incurs negligible additional cost over standard generation, and requires no retraining or fine-tuning of the generative model.