# MolPIF: A Parameter Interpolation Flow Model for Molecule Generation

arXiv: https://arxiv.org/abs/2507.13762 · HTML: https://mlsanity.com/paper/2507.13762/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 92 references that are in the map.
- First posted on arXiv 18 Jul 2025.

## Builds on (most cited first, 30 of 39)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Infinity: Scaling Bitwise AutoRegressive Modeling for High-Resolution Image Synthesis](https://mlsanity.com/paper/2412.04431/) (2024)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [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)
- [A 3D Generative Model for Structure-Based Drug Design](https://mlsanity.com/paper/2203.10446/) (2022)
- [Dirichlet Flow Matching with Applications to DNA Sequence Design](https://mlsanity.com/paper/2402.05841/) (2024)
- [DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design](https://mlsanity.com/paper/2403.07902/) (2024)
- [Generating 3D Molecules Conditional on Receptor Binding Sites with Deep Generative Models](https://mlsanity.com/paper/2110.15200/) (2021)
- [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)
- [Categorical Flow Matching on Statistical Manifolds](https://mlsanity.com/paper/2405.16441/) (2024)
- [Structure-based drug design with geometric deep learning](https://mlsanity.com/paper/2210.11250/) (2022)
- [Unifying Bayesian Flow Networks and Diffusion Models through Stochastic Differential Equations](https://mlsanity.com/paper/2404.15766/) (2024)
- [AudioX: A Unified Framework for Anything-to-Audio Generation](https://mlsanity.com/paper/2503.10522/) (2025)
- [Aligning Target-Aware Molecule Diffusion Models with Exact Energy Optimization](https://mlsanity.com/paper/2407.01648/) (2024)
- [CBGBench: Fill in the Blank of Protein-Molecule Complex Binding Graph](https://mlsanity.com/paper/2406.10840/) (2024)
- [FLOWR: Flow Matching for Structure-Aware De Novo, Interaction- and Fragment-Based Ligand Generation](https://mlsanity.com/paper/2504.10564/) (2025)
- [A Periodic Bayesian Flow for Material Generation](https://mlsanity.com/paper/2502.02016/) (2025)
- [CacheQuant: Comprehensively Accelerated Diffusion Models](https://mlsanity.com/paper/2503.01323/) (2025)

## Built on by (most cited first, 1 of 1)

- [EvoEGF-Mol: Evolving Exponential Geodesic Flow for Structure-based Drug Design](https://mlsanity.com/paper/2601.22466/) (2026)

## Abstract (arXiv)

Motivation: Structure-based drug design (SBDD) has advanced with deep generative models, but bridging the gap between continuous atomic coordinates and discrete atom types remains a challenge. Current approaches, such as diffusion and flow matching models, often fail to unify these heterogeneous modalities, relying on separate strategies or ill-fitting Euclidean metrics for discrete variables. This lack of a consistent framework limits generative models' ability to capture the geometric and chemical structure of protein-ligand complexes. Results: We present MolPIF, a parameter interpolation flow mechanism designed to unify the generation of continuous and discrete molecular variables. Unlike traditional flow models that operate in sample space, MolPIF interpolates between distributions in the parameter space, theoretically recovering Wasserstein-2 optimal transport for continuous coordinates and establishing Fisher-Rao geodesics for discrete atom types. We further incorporate a geometry-enhanced learning strategy to improve the capture of atomic contexts. Extensive evaluations on the CrossDocked2020 dataset demonstrate that MolPIF outperforms baselines in binding affinity, chemical validity, geometric fidelity and chemical space coverage. Additionally, MolPIF exhibits versatility in lead optimization and offers flexible prior distribution selection (such as Laplace), establishing a robust paradigm for SBDD. Availability: Source code is freely available at https://github.com/BLEACH366/MolPIF. Supplementary information: Supplementary data are available at Bioinformatics.