# Monte Carlo Tree Diffusion with Multiple Experts for Protein Design

arXiv: https://arxiv.org/abs/2509.15796 · HTML: https://mlsanity.com/paper/2509.15796/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 44 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Directly Fine-Tuning Diffusion Models on Differentiable Rewards](https://mlsanity.com/paper/2309.17400/) (2023)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [ReFT: Reasoning with Reinforced Fine-Tuning](https://mlsanity.com/paper/2401.08967/) (2024)
- [Planning with Large Language Models for Code Generation](https://mlsanity.com/paper/2303.05510/) (2023)
- [SE(3)-Stochastic Flow Matching for Protein Backbone Generation](https://mlsanity.com/paper/2310.02391/) (2023)
- [Diffusion Language Models Are Versatile Protein Learners](https://mlsanity.com/paper/2402.18567/) (2024)
- [Proteina: Scaling Flow-based Protein Structure Generative Models](https://mlsanity.com/paper/2503.00710/) (2025)
- [DPLM-2: A Multimodal Diffusion Protein Language Model](https://mlsanity.com/paper/2410.13782/) (2024)
- [EigenFold: Generative Protein Structure Prediction with Diffusion Models](https://mlsanity.com/paper/2304.02198/) (2023)
- [Don't throw away your value model! Generating more preferable text with Value-Guided Monte-Carlo Tree Search decoding](https://mlsanity.com/paper/2309.15028/) (2023)
- [Improved motif-scaffolding with SE(3) flow matching](https://mlsanity.com/paper/2401.04082/) (2024)
- [PepTune: De Novo Generation of Therapeutic Peptides with Multi-Objective-Guided Discrete Diffusion](https://mlsanity.com/paper/2412.17780/) (2024)
- [Multi-Architecture Multi-Expert Diffusion Models](https://mlsanity.com/paper/2306.04990/) (2023)
- [Monte Carlo Tree Diffusion for System 2 Planning](https://mlsanity.com/paper/2502.07202/) (2025)
- [RethinkMCTS: Refining Erroneous Thoughts in Monte Carlo Tree Search for Code Generation](https://mlsanity.com/paper/2409.09584/) (2024)
- [Blending Imitation and Reinforcement Learning for Robust Policy Improvement](https://mlsanity.com/paper/2310.01737/) (2023)
- [Active Policy Improvement from Multiple Black-box Oracles](https://mlsanity.com/paper/2306.10259/) (2023)
- [Discovering Mathematical Formulas from Data via GPT-guided Monte Carlo Tree Search](https://mlsanity.com/paper/2401.14424/) (2024)
- [Entropy-Reinforced Planning with Large Language Models for Drug Discovery](https://mlsanity.com/paper/2406.07025/) (2024)
- [DrugImproverGPT: A Large Language Model for Drug Optimization with Fine-Tuning via Structured Policy Optimization](https://mlsanity.com/paper/2502.07237/) (2025)
- [ProtInvTree: Deliberate Protein Inverse Folding with Reward-guided Tree Search](https://mlsanity.com/paper/2506.00925/) (2025)
- [Remix-DiT: Mixing Diffusion Transformers for Multi-Expert Denoising](https://mlsanity.com/paper/2412.05628/) (2024)
- [Contextual Active Model Selection](https://mlsanity.com/paper/2207.06030/) (2022)

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

- [Protein Thoughts: Interpretable Reasoning with Tree of Thoughts and Embedding-Space Flow Matching for Protein-Protein Interaction Discovery](https://mlsanity.com/paper/2605.21522/) (2026)
- [Leveraging generative hallucination and biophysics-informed modeling for unified biomolecular sequence-structure co-design](https://mlsanity.com/paper/2608.17381/) (2026)

## Abstract (arXiv)

The goal of protein design is to generate amino acid sequences that fold into functional structures with desired properties. Prior methods combining autoregressive language models with Monte Carlo Tree Search (MCTS) struggle with long-range dependencies and suffer from an impractically large search space. We propose MCTD-ME, Monte Carlo Tree Diffusion with Multiple Experts, which integrates masked diffusion models with tree search to enable multi-token planning and efficient exploration under the guidance of multiple experts. Unlike autoregressive planners, MCTD-ME uses biophysical-fidelity-enhanced diffusion denoising as the rollout engine, jointly revising multiple positions and scaling to large sequence spaces. It further leverages experts of varying capacities to enrich exploration, guided by a pLDDT-based masking schedule that targets low-confidence regions while preserving reliable residues. We propose a novel multi-expert selection rule ( PH-UCT-ME) extends Shannon-entropy-based UCT to expert ensembles with mutual information. MCTD-ME achieves superior performance on the CAMEO and PDB benchmarks, excelling in protein design tasks such as inverse folding, folding, and conditional design challenges like motif scaffolding on lead optimization tasks. Our framework is model-agnostic, plug-and-play, and extensible to denovo protein engineering and beyond.