# Demystifying Multimodal Biomolecular Co-design With Intrinsic Geodesic Coupling

arXiv: https://arxiv.org/abs/2606.01628 · HTML: https://mlsanity.com/paper/2606.01628/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 44 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Builds on (most cited first, 21 of 21)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pockets](https://mlsanity.com/paper/2205.07249/) (2022)
- [3D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Prediction](https://mlsanity.com/paper/2303.03543/) (2023)
- [ProGen2: Exploring the Boundaries of Protein Language Models](https://mlsanity.com/paper/2206.13517/) (2022)
- [SE(3)-Stochastic Flow Matching for Protein Backbone Generation](https://mlsanity.com/paper/2310.02391/) (2023)
- [A 3D Generative Model for Structure-Based Drug Design](https://mlsanity.com/paper/2203.10446/) (2022)
- [ProGen: Language Modeling for Protein Generation](https://mlsanity.com/paper/2004.03497/) (2020)
- [Diffusion Language Models Are Versatile Protein Learners](https://mlsanity.com/paper/2402.18567/) (2024)
- [DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design](https://mlsanity.com/paper/2403.07902/) (2024)
- [DPLM-2: A Multimodal Diffusion Protein Language Model](https://mlsanity.com/paper/2410.13782/) (2024)
- [Bayesian Flow Networks](https://mlsanity.com/paper/2308.07037/) (2023)
- [MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space](https://mlsanity.com/paper/2404.12141/) (2024)
- [La-Proteina: Atomistic Protein Generation via Partially Latent Flow Matching](https://mlsanity.com/paper/2507.09466/) (2025)
- [ProteinBench: A Holistic Evaluation of Protein Foundation Models](https://mlsanity.com/paper/2409.06744/) (2024)
- [Multi-domain Distribution Learning for De Novo Drug Design](https://mlsanity.com/paper/2508.17815/) (2025)
- [Piloting Structure-Based Drug Design via Modality-Specific Optimal Schedule](https://mlsanity.com/paper/2505.07286/) (2025)

## Abstract (arXiv)

Biomolecules such as proteins and small-molecule ligands play a central role in biological systems, arising from the tight interplay between sequence and three-dimensional structure. Recent generative models for biomolecular co-design aim to capture this interplay by jointly modeling coupled modalities. However, existing approaches largely adopt a parallel execution of marginal generative processes, implicitly enforcing fixed synchronous coupling. We argue that a critical but overlooked degree of freedom lies in how these marginal processes are temporally coupled during training and generation, where inappropriate coupling can introduce high-variance supervision and inconsistent intermediate states, affecting modality consistency. To address this, we introduce GeoCoupling, a systematic framework that optimizes for temporal couplings between heterogeneous modalities. Empirical results across structure-based drug design and unconditional protein design demonstrate the learned couplings consistently outperform synchronous and randomly coupled baselines, yielding biomolecules with improved physical validity and diversity.