# A Variational Perspective on Generative Protein Fitness Optimization

arXiv: https://arxiv.org/abs/2501.19200 · HTML: https://mlsanity.com/paper/2501.19200/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 43 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Builds on (most cited first, 24 of 24)

- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [Conditioning by adaptive sampling for robust design](https://mlsanity.com/paper/1901.10060/) (2019)
- [Guided Flows for Generative Modeling and Decision Making](https://mlsanity.com/paper/2311.13443/) (2023)
- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [Conservative Objective Models for Effective Offline Model-Based Optimization](https://mlsanity.com/paper/2107.06882/) (2021)
- [Taming VAEs](https://mlsanity.com/paper/1810.00597/) (2018)
- [Tranception: protein fitness prediction with autoregressive transformers and inference-time retrieval](https://mlsanity.com/paper/2205.13760/) (2022)
- [AdaLead: A simple and robust adaptive greedy search algorithm for sequence design](https://mlsanity.com/paper/2010.02141/) (2020)
- [The reparameterization trick for acquisition functions](https://mlsanity.com/paper/1712.00424/) (2017)
- [Plug & Play Directed Evolution of Proteins with Gradient-based Discrete MCMC](https://mlsanity.com/paper/2212.09925/) (2022)
- [Robust Optimization in Protein Fitness Landscapes Using Reinforcement Learning in Latent Space](https://mlsanity.com/paper/2405.18986/) (2024)
- [Closed-Form Test Functions for Biophysical Sequence Optimization Algorithms](https://mlsanity.com/paper/2407.00236/) (2024)
- [A primer on model-guided exploration of fitness landscapes for biological sequence design](https://mlsanity.com/paper/2010.10614/) (2020)

## Built on by (most cited first, 4 of 4)

- [Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modeling](https://mlsanity.com/paper/2504.10612/) (2025)
- [Repurposing Protein Language Models for Latent Flow-Based Fitness Optimization](https://mlsanity.com/paper/2602.02425/) (2026)
- [Feedback-Calibrated Protein Optimization with Batch-Aligned Tail Arbitration](https://mlsanity.com/paper/2609.37808/) (2026)
- [Structure-aware Reinforcement Learning for Protein Directed Evolution](https://mlsanity.com/paper/2609.39048/) (2026)

## Abstract (arXiv)

The goal of protein fitness optimization is to discover new protein variants with enhanced fitness for a given use. The vast search space and the sparsely populated fitness landscape, along with the discrete nature of protein sequences, pose significant challenges when trying to determine the gradient towards configurations with higher fitness. We introduce Variational Latent Generative Protein Optimization (VLGPO), a variational perspective on fitness optimization. Our method embeds protein sequences in a continuous latent space to enable efficient sampling from the fitness distribution and combines a (learned) flow matching prior over sequence mutations with a fitness predictor to guide optimization towards sequences with high fitness. VLGPO achieves state-of-the-art results on two different protein benchmarks of varying complexity. Moreover, the variational design with explicit prior and likelihood functions offers a flexible plug-and-play framework that can be easily customized to suit various protein design tasks.