# FP-AbDiff: Improving Score-based Antibody Design by Capturing Nonequilibrium Dynamics through the Underlying Fokker-Planck Equation

arXiv: https://arxiv.org/abs/2511.03113 · HTML: https://mlsanity.com/paper/2511.03113/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 5 Nov 2025.

## Builds on (most cited first, 14 of 14)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [A micro Lie theory for state estimation in robotics](https://mlsanity.com/paper/1812.01537/) (2018)
- [Provably Strict Generalisation Benefit for Equivariant Models](https://mlsanity.com/paper/2102.10333/) (2021)
- [Conditional Antibody Design as 3D Equivariant Graph Translation](https://mlsanity.com/paper/2208.06073/) (2022)
- [Deciphering antibody affinity maturation with language models and weakly supervised learning](https://mlsanity.com/paper/2112.07782/) (2021)
- [End-to-End Full-Atom Antibody Design](https://mlsanity.com/paper/2302.00203/) (2023)
- [AbDiffuser: Full-Atom Generation of in vitro Functioning Antibodies](https://mlsanity.com/paper/2308.05027/) (2023)
- [Expanding Expressiveness of Diffusion Models with Limited Data via Self-Distillation based Fine-Tuning](https://mlsanity.com/paper/2311.01018/) (2023)
- [Text-guided multi-property molecular optimization with a diffusion language model](https://mlsanity.com/paper/2410.13597/) (2024)
- [Antibody Design and Optimization with Multi-scale Equivariant Graph Diffusion Models for Accurate Complex Antigen Binding](https://mlsanity.com/paper/2506.20957/) (2025)

## Abstract (arXiv)

Computational antibody design holds immense promise for therapeutic discovery, yet existing generative models are fundamentally limited by two core challenges: (i) a lack of dynamical consistency, which yields physically implausible structures, and (ii) poor generalization due to data scarcity and structural bias. We introduce FP-AbDiff, the first antibody generator to enforce Fokker-Planck Equation (FPE) physics along the entire generative trajectory. Our method minimizes a novel FPE residual loss over the mixed manifold of CDR geometries (R3 x SO(3)), compelling locally-learned denoising scores to assemble into a globally coherent probability flow. This physics-informed regularizer is synergistically integrated with deep biological priors within a state-of-the-art SE(3)-equivariant diffusion framework. Rigorous evaluation on the RAbD benchmark confirms that FP-AbDiff establishes a new state-of-the-art. In de novo CDR-H3 design, it achieves a mean Root Mean Square Deviation of 0.99 AA when superposing on the variable region, a 25% improvement over the previous state-of-the-art model, AbX, and the highest reported Contact Amino Acid Recovery of 39.91%. This superiority is underscored in the more challenging six-CDR co-design task, where our model delivers consistently superior geometric precision, cutting the average full-chain Root Mean Square Deviation by ~15%, and crucially, achieves the highest full-chain Amino Acid Recovery on the functionally dominant CDR-H3 loop (45.67%). By aligning generative dynamics with physical laws, FP-AbDiff enhances robustness and generalizability, establishing a principled approach for physically faithful and functionally viable antibody design.