Steering Generative Models with Experimental Data for Protein Fitness Optimization

We thank the reviewer for their feedback on our work. We respond to the specific comments below:

W1: “The paper is not well-organised, making it difficult to read. The language should be carefully polished.”

Our Response: We appreciate this feedback and will revise the manuscript to improve its clarity and organization. In particular, we plan to streamline the presentation of our experimental findings and rephrase several technical descriptions to ensure they are more accessible. If there are specific sections or passages that the reviewer found especially difficult to follow, we would be grateful for any pointers to help focus our revisions more effectively.

W2: “Adding more datasets would strengthen the generality of the paper’s conclusions.”

Our Response: Thank you for this suggestion. To strengthen the conclusions from our paper and better demonstrate the generalization ability of our method, we have added a third case study using the GB1 dataset [1], which is commonly used in the protein design literature. Unlike TrpB and CreiLOV, GB1 has a much smaller multiple sequence alignment (only 126 sequences), making it significantly more challenging in the low-data regime. Despite this, our methods continue to perform strongly on GB1. In particular:

1. DAPS consistently steers generation toward high-fitness variants, even with limited data, and does so while maintaining sequence diversity.
2. In adaptive optimization experiments, DAPS significantly outperforms CG and other baselines, reinforcing its robustness and effectiveness across different tasks.

These new results further highlight the versatility of our framework and position DAPS as the strongest overall method in our evaluation. Figures 4–6 will be updated in the revision to include the GB1 results. For now, we provide a preview in tabular form below.

GB1 Results Table 1

GB1 Results Table 2

W3: “All results rely on an in-silico oracle, and no new wet-lab validation is provided.”

Our Response: We agree that wet-lab validation is an important next step. However, the scope of our study, which evaluates a broad range of design choices, makes comprehensive experimental validation intractable. In practice, wet-lab experiments are typically designed to validate a single modeling hypothesis due to cost and throughput constraints [2]. That said, we are actively pursuing collaborations to evaluate top-performing methods from our benchmark in targeted experimental campaigns.

W4: Additional citation.

Our Response: We have now additionally included the EvoDiff citation in Table 3.

Q1: “In Fig. 3, the authors points out many conbination among prior, learning strategy, and steering methods, but this study just discussed some of them. What about the remaining approaches?”

Our Response: We elected to provide readers with a broad overview of the methods that fall under the umbrella of SGPO. In our study, we focused on a manageable number of plug-and-play guidance strategies, which have low computational costs and are easy and practical for real-world engineering campaigns, compared to fine-tuning approaches. Future work could implement and compare the other approaches.

Q2: “In your experiments, why D3PM and MDLM models with the CG and DAPS guidance strategies achieved the best performance? Could you provide deeper explaination?”

Our Response: We found that DAPS is the best steering strategy overall, consistently outperforming other guidance strategies such as CG and NOS. This may be because the classifier used in DAPS is only trained on clean data, whereas CG requires training the classifier on both clean and noisy data. We also found that the D3PM and MDLM models are better suited for discrete data, as they are able to capture the natural distribution of protein sequences, compared to the continuous model. Thus, for real world applications, we would suggest using DAPS + D3PM/MDLM.

L1: “The paper would benefit by providing the source code for reviewers…”

Our Response: We have developed a comprehensive and well-organized codebase that is already publicly available on a GitHub repository. However, due to this year’s rebuttal policy, we are unable to share the link at this stage.

Please let us know if you have any further feedback or questions!

Citations:

[1] Olson, C. A.; Wu, N. C.; Sun, R. A Comprehensive Biophysical Description of Pairwise Epistasis throughout an Entire Protein Domain. Current Biology 2014, 24 (22), 2643–2651.

[2] Yang, J.; Lal, R. G.; Bowden, J. C.; Astudillo, R.; Hameedi, M. A.; Kaur, S.; Hill, M.; Yue, Y.; Arnold, F. H. Active Learning-Assisted Directed Evolution. Nat Commun 2025, 16 (1), 714.

We thank the reviewer for their feedback and for their support of our work. We respond to the specific comments below:

W1: “There is little methodological novelty in the paper…”

Our Response: We respectfully disagree with the claim that the paper lacks methodological novelty. While our focus is not on proposing a new generative model or steering algorithm, our main contribution lies in the conceptual unification and rigorous comparative evaluation of a broad class of steering techniques that have emerged in recent years but have largely been studied in isolation. Our SGPO framework draws meaningful connections between approaches from classifier guidance, Bayesian optimization, and reinforcement learning, and enables their systematic evaluation across multiple generative models and tasks.

W2: “There is no wet-lab validation…”

Our Response: We agree that wet-lab validation is an important next step. However, the scope of our study, which evaluates a broad range of design choices, makes comprehensive experimental validation intractable. In practice, wet-lab experiments are typically designed to validate a single modeling hypothesis due to cost and throughput constraints [1]. That said, we are actively pursuing collaborations to evaluate top-performing methods from our benchmark in targeted experimental campaigns.

W3: “The paper only studies two different protein optimization tasks and it is not entirely clear how generalizable the results are to other tasks. ”

Our Response: Prior to our study, it was not clear that DAPS + D3PM/MDLM would be such a strong model, consistently outperforming baselines such as NOS and DPO, which we believe is a valuable insight to both ML researchers looking to guide discrete diffusion models and protein engineers looking to choose a strategy for wet lab campaigns. To strengthen this conclusion, we have added a third case study using the GB1 dataset [2], which is commonly used in the protein design literature. Unlike TrpB and CreiLOV, GB1 has a much smaller multiple sequence alignment (only 126 sequences), making it significantly more challenging in the low-data regime. Despite this, our methods continue to perform strongly on GB1. In particular:

1. DAPS consistently steers generation toward high-fitness variants, even with limited data, and does so while maintaining sequence diversity.
2. In adaptive optimization experiments, DAPS significantly outperforms CG and other baselines, reinforcing its robustness and effectiveness across different tasks.

These new results further highlight the versatility of our framework and position DAPS as the strongest overall method in our evaluation. Figures 4–6 will be updated in the revision to include the GB1 results. For now, we provide a preview in tabular form below.

GB1 Results Table 1

GB1 Results Table 2

W4: “While it is cumbersome and challenging to tune those hyperparameters, I would expect the authors to study method tuning in depth”

Our Response: Thank you for this suggestion. We have now included a more comprehensive hyperparameter search over 30 combinations of NOS hyperparameters, following previous studies [3–4], across num_steps = 5, 10; step_size = 0.5, 2, 5; and stability_coefficient = 0.1, 1, 10, 100, 1000. Fig. 5 will be updated in the revision, but in the meantime we report the performance of the top 2 hyperparameter configurations in the table below, compared to DAPS with an optimized guidance strength. These new results corroborate our previous findings, confirming that DAPS methods consistently outperform NOS.

NOS Hyperparameters Results Table

For DPO, we have also performed a more detailed hyperparameter search over the “ranked” and “weighted” loss variants, and this comparison will be included in the revision. Overall, we found that DPO still does not enable much steerability, with both loss forms performing similarly.

Please let us know if you have any further feedback or questions!

Citations:

[1] Yang, J.; Lal, R. G.; Bowden, J. C.; Astudillo, R.; Hameedi, M. A.; Kaur, S.; Hill, M.; Yue, Y.; Arnold, F. H. Active Learning-Assisted Directed Evolution. Nat Commun 2025, 16 (1), 714.

[2] Olson, C. A.; Wu, N. C.; Sun, R. A Comprehensive Biophysical Description of Pairwise Epistasis throughout an Entire Protein Domain. Current Biology 2014, 24 (22), 2643–2651.

[3] Gruver, N.; Stanton, S.; Frey, N. C.; Rudner, T. G. J.; Hotzel, I.; Lafrance-Vanasse, J.; Rajpal, A.; Cho, K.; Wilson, A. G. Protein Design with Guided Discrete Diffusion. In Advances in Neural Information Processing Systems 36; 2023.

[4] Schiff, Y.; Sahoo, S. S.; Phung, H.; Wang, G.; Boshar, S.; Dalla-torre, H.; Almeida, B. P. de; Rush, A.; Pierrot, T.; Kuleshov, V. Simple Guidance Mechanisms for Discrete Diffusion Models. In Thirteenth International Conference on Learning Representations, 2025.

We thank the reviewer for their constructive feedback and for their support of our work. We respond to the specific comments below:

W1: “Please discuss this [latent BO] line of work and clearly differentiate your work within this context.”

Our Response: Thank you for raising this important point. We agree that adaptive optimization with labeled fitness data is standard in the Bayesian optimization (BO) community, and we appreciate your suggestion to clarify how our work relates to this literature.

Our goal in introducing SGPO is to unify and systematize a broad class of emerging techniques, including classifier guidance, posterior sampling, and reinforcement learning, for guiding generative protein models with labeled data. Many of these approaches, particularly in the protein modeling community, are not typically framed in BO terms. SGPO provides a coherent perspective that connects these different lines of work.

That said, we agree that SGPO is closely related to prior work combining BO with deep generative models that you have suggested, and we will revise the manuscript to clarify these connections. In particular, we will contrast SGPO with latent-space BO approaches and highlight key differences. SGPO offers greater flexibility by avoiding reliance on an explicit latent space, which enables the use of modern, more powerful generative models such as diffusion models and protein language models that are not easily accommodated by traditional latent BO pipelines. In response to your suggestion, we have also added APEX-GO (based on LOL-BO) from Torres et al. [1] as a representative baseline from the latent-space BO class of algorithms.

The approach of Gruver et al. [2] can be viewed as an instance within our broader SGPO framework. SGPO supports a wider range of generative models and steering strategies, and this generality is reflected in the substantial empirical improvements achieved by several of our proposed methods over NOS, the guidance technique introduced in [2].

W2: “I think the paper should invest more effort in making the baselines strong.”

Our Response: Thank you for this suggestion. We have now included a more comprehensive hyperparameter search over 30 combinations of NOS hyperparameters following previous studies [2-3], across num_steps=5,10; step_size= 0.5,2,5; and stability_coefficient=0.1,1,10,100,1000. Fig. 5 will be updated in the revision, but in the meantime we report the performance of the top 2 ideal combinations of NOS hyperparameters in the table below, compared to the performance of DAPS with an optimized guidance strength. Ultimately, these new results corroborate previously reported results, confirming that DAPS methods perform better than NOS.

NOS Hyperparameters Results Table

To better demonstrate the generalizability of our methods, we have added a third case study using the GB1 dataset [4], which is commonly used in the protein design literature. Unlike TrpB and CreiLOV, GB1 has a much smaller multiple sequence alignment (only 126 sequences), making it significantly more challenging in the low-data regime. Despite this, our methods continue to perform strongly on GB1. In particular:

1. DAPS consistently steers generation toward high-fitness variants, even with limited data, and does so while maintaining sequence diversity.
2. In adaptive optimization experiments, DAPS significantly outperforms CG and other baselines, reinforcing its robustness and effectiveness across different tasks.

These new results further highlight the versatility of our framework and position DAPS as the strongest overall method in our evaluation. Figures 4–6 will be updated in the revision to include the GB1 results. For now, we provide a preview in tabular form below.

GB1 Results Table 1

GB1 Results Table 2

W3: “Strong baselines like NOS, LOL-BO were not included in the adaptive optimization part of the results. Please consider including them.”

Our Response: We have now included NOS in the adaptive optimization experiments, and it continues to underperform relative to CG and DAPS. In addition, we have incorporated APEX-GO [1] (a recent protein-specific instantiation of LOL-BO) as a representative latent-space BO method. Initial results across all three datasets suggest that APEX-GO performs poorly in this setting (see the table below for GB1 adaptive optimization results). We hypothesize that this may be due to (i) the longer sequences used in our work compared to original LOL-BO studies, and (ii) the difficulty in calibrating the trust region in very low-data regimes with limited rounds of optimization. We will provide a more thorough discussion of these limitations in the revised manuscript and will also update Figure 6 to reflect these new results.

APEXGO Results Table

W4+5: Concerns about statements in Lines 58 and 150.

Our Response: We have rewritten the specific sentence mentioned in line 58 and removed the sentence mentioned in line 150 to characterize existing work more accurately.

W6: “The choice of DPO in this setting seems a bit unclear since it converts absolute fitness values into pairwise preference …”

Our Response: We explored two different DPO implementations using the “ranked” and “weighted” loss forms as outlined in [5]. Namely, the weighted form is able to capture absolute fitness values. We have now performed a more detailed hyperparameter search over these two types of models, and this comparison will be included in the revision. Overall, we found that DPO still does not enable much steerability, with “ranked” and “weighted” loss forms performing similarly.

W7: “I find the justification for TrPB dataset in Table 2 a bit surprising”

Our Response: We appreciate the opportunity to clarify. Our intention was not to suggest that TrpB is uninteresting, but rather to note that the complexity of its fitness landscape (due to significant epistasis) poses a challenge despite the availability of many labeled sequences. We agree with the reviewer that such complexity is precisely what makes TrpB a valuable benchmark for testing generative modeling strategies. We have revised the phrasing accordingly.

We thank the reviewer again for their constructive suggestions. We believe the revised manuscript will be significantly strengthened as a result of your feedback. Please let us know if there are any further points you'd like us to address.

Citations:

[1] Torres, M. D. T.; Zeng, Y.; Wan, F.; Maus, N.; Gardner, J.; De La Fuente-Nunez, C. A Generative Artificial Intelligence Approach for Antibiotic Optimization. bioRxiv, 2024.

[2] Gruver, N.; Stanton, S.; Frey, N. C.; Rudner, T. G. J.; Hotzel, I.; Lafrance-Vanasse, J.; Rajpal, A.; Cho, K.; Wilson, A. G. Protein Design with Guided Discrete Diffusion. In Advances in Neural Information Processing Systems 36; 2023.

[3] Schiff, Y.; Sahoo, S. S.; Phung, H.; Wang, G.; Boshar, S.; Dalla-torre, H.; Almeida, B. P. de; Rush, A.; Pierrot, T.; Kuleshov, V. Simple Guidance Mechanisms for Discrete Diffusion Models. In Thirteenth International Conference on Learning Representations, 2025.

[4] Olson, C. A.; Wu, N. C.; Sun, R. A Comprehensive Biophysical Description of Pairwise Epistasis throughout an Entire Protein Domain. Current Biology 2014, 24 (22), 2643–2651.

[5] Stocco, F.; Artigues-Lleixà, M.; Hunklinger, A.; Widatalla, T.; Güell, M.; Ferruz, N. Guiding Generative Protein Language Models with Reinforcement Learning. arXiv 2025.

First, we thank the reviewer again for their thoughtful feedback and for increasing their score. We address the follow-up comments below.

“I think this is a strong point of the paper and a valuable contribution to the community.”

Our response: Thank you for this generous comment. We are glad you found the unifying perspective of SGPO to be a valuable contribution. We will emphasize this aspect more clearly in the revision and further elaborate on its conceptual connections to prior work.

“Thanks for adding the new baseline of Torres et al [1]. This is a stronger baseline and great to see the results still hold up well.”

Our response: We appreciate the suggestion to include baselines from the latent space BO literature. We are pleased that the results continue to support the strength of SGPO methods and will highlight this comparison in the revised manuscript.

“I request the authors to spend more time and dig a bit deeper on this discussion since it will significantly strengthen the paper.”

Our response: Thank you for encouraging us to clarify the relationship between SGPO and prior work on Bayesian optimization with generative models. We agree that making these connections more explicit will significantly strengthen the paper, and we will revise the manuscript accordingly.

While both SGPO and latent space BO aim to leverage generative models for guided sequence design, they differ in how the optimization process is structured. Latent space BO methods typically define an explicit optimization problem in a learned latent space: a surrogate model is trained to predict outcomes based on latent codes, and acquisition functions are optimized to select promising codes, which are then decoded. This approach provides a well-defined optimization landscape but relies heavily on the structure of the latent space learned during generative model training. In protein design, such latent spaces are often shaped by distributions over natural sequences, which can limit extrapolation to high-fitness but unnatural variants. Prior work (e.g., Maus et al., 2022) has shown that latent BO can underperform when the latent space is not well aligned with the property being optimized. One possible remedy is to fine-tune the generative model using objective values in an end-to-end fashion, but this can be computationally expensive and may introduce additional challenges, such as overfitting or mode collapse.

SGPO, by contrast, steers generation directly in sequence space using posterior-guided sampling. This avoids the need for a fixed latent space and supports a broader range of generative models, including diffusion models and protein language models without encoder-decoder architectures. It also enables plug-and-play use of scoring models trained solely on labeled data, allowing for greater adaptability to new objectives. That said, we believe there is promising future work in incorporating ideas from latent BO, such as local surrogate modeling, within the SGPO framework.

The case of NOS (Gruver et al., 2023) is particularly interesting. Although NOS perturbs internal activations of the denoising network—effectively manipulating a latent representation—it does not optimize an acquisition function in this space as traditional latent BO methods do. Instead, its mechanism resembles classifier guidance, modifying the generative trajectory during sampling. For this reason, we view NOS as conceptually closer to SGPO than to latent BO. Nevertheless, our experiments show that NOS underperforms relative to SGPO methods like DAPS and CG. We believe that DAPS’s strong performance can be explained by the fact that DAPS leverages a classifier trained only on clean data and applies input-level guidance.

We will revise the manuscript to incorporate this expanded discussion, clarify conceptual distinctions, and cite the relevant literature.

“I am not asking for new results but just curious if there is no standardized benchmark yet in protein sequence design?”

Our response: Indeed, there is currently no standardized oracle or dataset for sequence-level protein design over a large combinatorial space, where the goal is to identify combinations of multiple mutations—not just predict single mutation effects, which is the focus of ProteinGym. While some prior studies have used datasets like AAV or GFP, the optimization tasks and oracles used are not standardized, and none explicitly leverage both natural sequence priors and labeled fitness data, as we do in our study. We chose to focus on TrpB and CreiLOV because they are newer and more challenging benchmarks. That said, we agree that developing a more comprehensive and standardized benchmark for protein sequence design is an important direction for future work.

We thank the reviewer for their constructive feedback and their support of our work. Below we address the specific concerns raised.

W1: “Results on a more diverse set of proteins or harder fitness objectives would significantly strengthen impact.”

Our response: We thank the reviewer for this suggestion. To better demonstrate the generalizability of our methods, we have added a third case study using the GB1 dataset [1], which is commonly used in the protein design literature. Unlike TrpB and CreiLOV, GB1 has a much smaller multiple sequence alignment (only 126 sequences), making it significantly more challenging in the low-data regime. Despite this, our methods continue to perform strongly on GB1. In particular:

1. DAPS consistently steers generation toward high-fitness variants, even with limited data, and does so while maintaining sequence diversity.
2. In adaptive optimization experiments, DAPS significantly outperforms CG and other baselines, reinforcing its robustness and effectiveness across different tasks.

These new results further highlight the versatility of our framework and position DAPS as the strongest overall method in our evaluation. Figures 4–6 will be updated in the revision to include the GB1 results. For now, we provide a preview in tabular form below.

GB1 Results Table 1

GB1 Results Table 2

W2/Q1: “Could the authors provide additional guidance on how practitioners should select or tune the guidance strength hyperparameter in real-world, held-out experimental campaigns?”

Our Response: Thank you for raising this important point. We would first like to emphasize that the methods explored in our study, such as CG and DAPS, are intentionally designed to be simple to tune, with only a single steering hyperparameter. This is in contrast to methods like NOS and DPO, which involve more complex and sensitive hyperparameter choices. We will add the following sentence to the revision to offer more concrete guidance:

“In real-world engineering scenarios, even in the absence of ground truth fitness labels, one practical approach to selecting the guidance strength is to scan over values and choose the highest setting for which the N generated sequences remain unique and novel relative to previously measured sequences, where N corresponds to the screening throughput available for the next round.”

This ensures that the chosen guidance strength balances optimization with diversity and remains actionable under practical experimental constraints.

Please let us know if you have any further feedback or questions!

Citations:

[1] Olson, C. A.; Wu, N. C.; Sun, R. A Comprehensive Biophysical Description of Pairwise Epistasis throughout an Entire Protein Domain. Current Biology 2014, 24 (22), 2643–2651.