# Diffusion Large Language Models for Black-Box Optimization

arXiv: https://arxiv.org/abs/2601.14446 · HTML: https://mlsanity.com/paper/2601.14446/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 51 references that are in the map.
- First posted on arXiv 20 Jan 2026.

## Builds on (most cited first, 30 of 40)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models](https://mlsanity.com/paper/2503.09573/) (2025)
- [MMaDA: Multimodal Large Diffusion Language Models](https://mlsanity.com/paper/2505.15809/) (2025)
- [Scaling up Masked Diffusion Models on Text](https://mlsanity.com/paper/2410.18514/) (2024)
- [DiffuCoder: Understanding and Improving Masked Diffusion Models for Code Generation](https://mlsanity.com/paper/2506.20639/) (2025)
- [Large Language Models as Evolutionary Optimizers](https://mlsanity.com/paper/2310.19046/) (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)
- [Learning Search Space Partition for Black-box Optimization using Monte Carlo Tree Search](https://mlsanity.com/paper/2007.00708/) (2020)
- [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)
- [Using Large Language Models for Hyperparameter Optimization](https://mlsanity.com/paper/2312.04528/) (2023)
- [RoMA: Robust Model Adaptation for Offline Model-based Optimization](https://mlsanity.com/paper/2110.14188/) (2021)
- [Offline Model-Based Optimization via Normalized Maximum Likelihood Estimation](https://mlsanity.com/paper/2102.07970/) (2021)
- [PepTune: De Novo Generation of Therapeutic Peptides with Multi-Objective-Guided Discrete Diffusion](https://mlsanity.com/paper/2412.17780/) (2024)
- [Generative Pretraining for Black-Box Optimization](https://mlsanity.com/paper/2206.10786/) (2022)
- [Diffusion Tree Sampling: Scalable inference-time alignment of diffusion models](https://mlsanity.com/paper/2506.20701/) (2025)
- [Monte Carlo Tree Diffusion for System 2 Planning](https://mlsanity.com/paper/2502.07202/) (2025)
- [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)
- [The Importance of Directional Feedback for LLM-based Optimizers](https://mlsanity.com/paper/2405.16434/) (2024)
- [LICO: Large Language Models for In-Context Molecular Optimization](https://mlsanity.com/paper/2406.18851/) (2024)
- [ExPT: Synthetic Pretraining for Few-Shot Experimental Design](https://mlsanity.com/paper/2310.19961/) (2023)

## Built on by (most cited first, 2 of 2)

- [Support-Proximity Augmented Diffusion Estimation for Offline Black-Box Optimization](https://mlsanity.com/paper/2605.11246/) (2026)
- [Large Discovery Models: Empirically-grounded Model-Based Open-Ended Search](https://mlsanity.com/paper/2608.15669/) (2026)

## Abstract (arXiv)

Offline black-box optimization (BBO) aims to find optimal designs based solely on an offline dataset of designs and their labels. Such scenarios frequently arise in domains like DNA sequence design and robotics, where only a few labeled data points are available. Traditional methods typically rely on task-specific proxy or generative models, overlooking the in-context learning capabilities of pre-trained large language models (LLMs). Recent efforts have adapted autoregressive LLMs to BBO by framing task descriptions and offline datasets as natural language prompts, enabling direct design generation. However, these designs often contain bidirectional dependencies, which left-to-right models struggle to capture. In this paper, we explore diffusion LLMs for BBO, leveraging their bidirectional modeling and iterative refinement capabilities. This motivates our in-context denoising module: we condition the diffusion LLM on the task description and the offline dataset, both formatted in natural language, and prompt it to denoise masked designs into improved candidates. To guide the generation toward high-performing designs, we introduce masked diffusion tree search, which casts the denoising process as a step-wise Monte Carlo Tree Search that dynamically balances exploration and exploitation. Each node represents a partially masked design, each denoising step is an action, and candidates are evaluated via expected improvement under a Gaussian Process trained on the offline dataset. Our method, dLLM, achieves state-of-the-art results in few-shot settings on design-bench.