Title: Generative property enhancer:  implicit guided generation through conditional density estimation
Venue: NeurIPS 2025
Accepted: yes
Keywords: generative modeling

drug discovery

design optimization
Abstract: Generative modeling is increasingly important for data-driven computational design. Conventional approaches pair a generative model with a discriminative model to select or guide samples toward optimized designs. Yet discriminative models often struggle in data-scarce settings, common in scientific applications, and are unreliable in the tails of the distribution where optimal designs typically lie. We introduce generative property enhancer (GPE), an approach that implicitly guides generation by matching samples with lower property values to higher-value ones. Formulated as conditional density estimation, our framework defines a target distribution with improved properties, compelling the generative model to produce enhanced, diverse designs without auxiliary predictors. GPE is simple, scalable, end-to-end, modality-agnostic, and integrates seamlessly with diverse generative model architectures and losses. We demonstrate competitive empirical results on standard _in silico_ offline (non-sequential) protein fitness optimization benchmarks. Finally, we propose iterative training on a combination of limited real data and self-generated synthetic data, enabling extrapolation beyond the original property ranges.

Generative property enhancer: implicit guided generation through conditional density estimation

Abstract

Generative modeling is increasingly important for data-driven computational design. Conventional approaches pair a generative model with a discriminative model to select or guide samples toward optimized designs. Yet discriminative models often struggle in data-scarce settings, common in scientific applications, and are unreliable in the tails of the distribution where optimal designs typically lie. We introduce generative property enhancer (GPE), an approach that implicitly guides generation by matching samples with lower property values to higher-value ones. Formulated as conditional density estimation, our framework defines a target distribution with improved properties, compelling the generative model to produce enhanced, diverse designs without auxiliary predictors. GPE is simple, scalable, end-to-end, modality-agnostic, and integrates seamlessly with diverse generative model architectures and losses. We demonstrate competitive empirical results on standard in silico offline (non-sequential) protein fitness optimization benchmarks. Finally, wepropose iterative training on a combination of limited real data and self-generated synthetic data, enabling extrapolation beyond the original property ranges.

1 Introduction

Generative modeling has become an essential component to tackle computational design problems in scientific applications such as protein engineering, synthetic biology, material sciences or molecular design. An important application-the one we explore in this work-is the problem of design optimization 1 , where the goal is to produce optimized samples (designs) according to some desired property(ies).

Conventional data-driven approaches are usually composed of two modules: (i) a generative model to propose design candidates, and (ii) a discriminative model to select optimized designs. The discriminative models are trained on available data to approximate the unknown objective landscape of the data. They are used to either rank and select generated samples or to guide the generation process toward samples with desired properties [1-18]. However, when data is scarce (usually the case in scientific applications), training a reliable discriminative model is often not feasible. To make the matter worse, we usually seek designs that lie in the tail of the distribution of the property which is typically very challenging to learn, making predictions even less reliable.

In this work, we challenge this paradigm by casting the problem of design optimization as a conditional generative modeling problem. We leverage the implicit guidance mechanismproposedbyTagasovskaet al. [19] and take it a step further by going from an optimization perspective to a sampling-based one. This transition allows us to move beyond generating single point estimates and instead estimate

Figure 1

(a) Dataset

(b) Unguided generation

(c) Implicit guided optimization (d) Implicit guided generation

(a) Dataset (b) Unguided generation (c) Implicit guided optimization (d) Implicit guided generation the probability density of improved designs. As a result, our framework is more general-readily applicable to diverse settings, data modalities, and generative models-and it mitigates a core limitation of point-based methods: their tendency to converge to local maxima [20, Section 4].

Our approachgenerative property enhancer (GPE) -utilizes inherent pairwise relationships within the data: by matching lower-valued property samples x directly to higher-valued samples x ′ , our method implicitly defines an improved target distribution . This 'matching' strategy naturally forms a conditional density estimation problem wherein the generative model is compelled-via e.g. maximum likelihood training or approximating conditional score functions-to reproduce the distribution of samples with improved properties. Thus, excluding the reliance on any external discriminative model 2 .

GPE provides an end-to-end, simple and scalable way to tackle design optimization problems with conditional generative models. The implicit guidance mechanism eliminates the need for an external predictor, reducing the complexity of the model and improving data efficiency. Moreover, it increases the effective training set size by taking into account pairs of points. Finally, our approach is general and can be applied to many different off-the-shelf state-of-the-art generative models and data modalities. Figure 1 shows how our approach works in an illustrative example and highlights its benefits compared to baselines.

Our contributions are as follows: (i) We propose a new implicitly guided generative framework and provide general theoretical guarantees (Section 3.1). (ii) We show how to incorporate the proposed implicit guidance within diverse off-the-shelf generative modeling frameworks, e.g., variational autoencoders [21], flow matching [22], and walk-jump sampling [23] (Section 3.2). (iii) We show empirically that GPE models achieve competitive results in an in silico benchmark for offline (non-sequential) protein fitness optimization in two well-studied protein domains (Section 4.1). (iv) Weshow how GPE can 'self train', pushing the boundaries of the designs' property beyond their scope in the training set (Section 4.2).

2 Related work

Most related works have been applied in the context of protein design and optimization. This problem has been tackled with a plethora of approaches, including latent space optimization [24, 11, 25, 15], reinforcement learning [6, 26, 15], genetic algorithm-based approaches [27, 8, 28, 29], energy-based methods [30, 31, 14], methods based on machine translation [32, 33, 12] and predictor-guided generative models [34, 7, 13, 35-39]. These approaches are typically deployed in either an offline setting, where optimization is performed on a fixed dataset, or an online setting involving iterative, multi-round optimization. While our work focuses on the former, we note that our model can be readily integrated into online frameworks, for instance, to warm-start the optimization or as a generative model to produce design candidates at each iteration.

Our work is closer to iterative editing methods, where the goal is to iteratively make local modifications to inputs for extrapolating the property of interest. For instance, Damani et al. [33] propose to continuously revising combinatorial structures on small molecules via paired data. Other works [12, 18] match sequences by generating perturbed sequences, scoring them with a (learned) scorer, and matching the original sequence with the generated ones (if the predicted score is below a certain threshold). Kirjner et al. [14] propose an approach where they iteratively use Gibbs sampling [40], followed by a scorer-based selection, on smoothed protein fitness landscapes. In contrast to previous work, GPE introduces a domain and modality-agnostic framework, comes with new theoretical guarantees that link generated samples to the property improvement. Moreover, unlike previous work, our method does not rely on discriminative models on any step of training, sampling or selection. Therefore, it can easily be integrated with previous work, potentially improving performance even further.

Our pairing step induces a preference relation, connecting our approach to preference learning [41], including DPO [42] for large language models, which shifts models toward preferred outcomes under (implicit) KL regularization. Recent protein-design work echoes this idea. Lee et al. [43] propose a fine-tuning framework to align protein language models to a specific desired fitness by ranking mutants. ReFT [44] filters data with auxiliary rewards and fine-tunes on the preferred subset for backbone generation. Zhou et al. [45] learns residue-level energy preferences to train a conditional diffusion model with a direct preference objective for antibody co-design and Mistani et al. [46] uses DPO on curated chosen-rejected receptor-binder pairs for peptide/protein binders. Despite these links, our setting differs from classical preference learning which compares pairs without enforcing proximity in data space or property magnitude.

Finally, we note that our contribution is orthogonal to classifier guidance [47] and classifier-free guidance [48] approaches, commonly used to guide diffusion models [49, 50] (and some instantiations of flow matching). In fact, our framework could seamlessly be integrated into both approaches, either by leveraging a trained classifier (classifier guidance) or by using the low-property seed as the conditioning signal (classifier-free guidance).

3 Implicit guided generation by data matching

3.1 Problem setting

Weaddresstheproblemof offline optimization [51, 52], also known as model-based optimization, where the goal is to optimize a black-box function using only a fixed, static dataset. This paradigm stands in contrast to online optimization approaches, such as active learning or Bayesian optimization, which iteratively query a ground-truth objective function to acquire new data and refine a surrogate model.

Our goal is to generate new samples, referred to as designs , given one or more lead data points, referred to as seeds . The key objectives are twofold: a generated design must improve upon its seed in a specific property of interest (e.g., the potency of a molecule) while also adhering to predefined constraints (e.g., a limited number of modifications).

More formally, let X be a design space representing either a d -dimensional continuous space, R d , or a discrete space of length L over a finite vocabulary V (e.g. for proteins | V | =20 ). Let g : X → R be a function that quantifies the property of interest. Given a seed x ∈ X , our objective is to generate new candidate designs x ′ ∈ X satisfying two conditions: (i) the designs' score must exceed that of the seed, g ( x ′ ) >g ( x ) , and (ii) the designs must satisfy a set of constraints, represented by a boolean function C ( x,x ′ ) . For example, this function could encode a bound on the distance between seed and design, C ( x,x ′ )= dist ( x,x ′ ) < ∆ x for some threshold ∆ x ∈ R + .

In this work, we cast the problem above as a conditional generation problem, i.e., learn how to sample from the improved distribution given an initial seed x :

where the indicator I ( x,x ′ ) is given by:

The normalizing factor Z ( x ) in (1) is generally intractable due to the (usually) high dimensionality of the data and it cannot be solved directly. The following theorem establishes a learning criterion for the improved distribution.

Theorem 1 (Optimality of implicit property enhancement) . Let p ( x ) be a probability distribution and p + ( x ′ | x ) its corresponding improved distribution, as defined in (1). Consider the objective functional:

where q ( · | x ) is any family of conditional densities with supp( p + ) ⊂ supp( q ) . Then, the objective L ( q ) has the unique minimizer:

Proof. Introduce a Lagrange multiplier λ ( x ) for the constraint ∫ q ( x ′ | x ) dx ′ =1 . The Lagrangian is defined as:

Taking the functional derivative w.r.t. q ( x ′ | x ) and setting it to zero gives:

Enforcing normalization ∫ q ( x ′ | x ) dx ′ = 1 forces λ ( x ) = 1 . Hence q ∗ ( x ′ | x ) = p + ( x ′ | x ) , as claimed.

We stress that the condition that the support of the variational density is greater than the support of the ground truth density is fairly standard in variational inference and can be easily ensured with appropriate architecture choices. Furthermore, we note that the proof is an adaptation of a similar approach for showing that maximum likelihood recovers the ground truth density at optimality.

Aone-dimensional example. Tobuild intuition, consider the following one-dimensional example: The data distribution p ( x ) is the standard normal and the property of interest is defined as g ( x )= -( x -1) 2 . For a given suboptimal sample y , the improved distribution is defined as p + ( x ′ | y ) ∝ p ( x ′ ) I ( g ( x ′ ) > g ( y ) ) . Wenowtry to compute the conditional expectation f ∗ ( y ) ≈ E [ x ′ | g ( x ′ ) >g ( y ) ] , the probability p ( g ( x ′ ) >g ( y ) ) , and comparison of the quality g ( y ) to the average quality of improved samples. From Figure 2, we observe a few things: (i) Conditional Expectation: When y is far from the optimal region ( x ≈ 1 ), the expected superior x ′ is significantly higher. As y nears the optimum, the improvement diminishes. (ii) Probability of Improvement: The likelihood of finding a superior sample decreases as y approaches the optimal quality and (iii) Quality Comparison: The plot shows that the improved samples not only exhibit higher x ′ values but also consistently have enhanced quality g ( x ′ ) relative to g ( y ) .

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3.2 Matched generative models

Given an initial dataset D = { ( x i , g ( x i ) } n i =1 , x i ∈ X , g ( x i ) ∈ R and a set of constraints C ( x,x ′ ) : X × X →{ True , False } , we construct a matched dataset M = { ( x i , x ′ i ) } N i =1 , following Tagasovska et al. [19]:

where x and x ′ are elements of D . By construction, M contains samples drawn from p + ( x ′ | x ) p ( x ) . Westress that typically the matched dataset M has the attractive property that it is significantly larger than the initial dataset D , i.e. N>n , which is a particularly desirable in the low-data regime.

Equipped with Theorem 1 and matched datasets (2), our goal is to learn a conditional generator q θ ( x ′ | x ) , parameterized by θ , that approximates the improved distribution p + ( x ′ | x ) . This is done by minimizing the following loss:

The minimization of L ( θ, M ) aligns the generative process with the desired improvement through conditional density estimation, bypassing the need for an explicit property predictor. In some cases (e.g. discrete data), one can directly parametrize the likelihood above. When that is not easily feasible, we resort to approximating it. Next, we show how we can adapt off-the-shelf models to sample from the conditional distribution of interest. We note that our approach is fairly general and can similarly be applied to other generative models, such as autoregressive or diffusion models.

Matched PropEn (mPropEn). PropEn [19] leverages matched datasets to approximate the gradient of the property of interest by minimizing a matched reconstruction loss, between a sample with low property and its higher-value match. The trained model is used to sample designs by 'following the gradient': given an initial seed, the model is applied iteratively, generating one sample per iteration step. When data is discrete, the matched reconstruction loss is the negative log-likelihood loss in (3). Here we extend the gradient-based PropEn into an instantiation of matched generative models 3 : we sample set of designs from the logits of the model (by choosing an appropriate temperature).

Matched variational auto-encoder (mVAE). We instantiate q θ ( x ′ | x ) as a latent-variable model defined as:

parameterized by θ =( ϕ,ψ ) , where ϕ and ψ are parameters of the encoder and decoder, respectively. Training is done by minimizing the following negative ELBO [21, 53]:

where N ( z ;0 ,I d ) is the standard d -dimensional normal distribution. This objective is a lower bound of the maximum-likelihood problem in Theorem 1. Hence, the mVAE approximates the optimal density while providing a tractable latent representation and sampling mechanism. We sample designs following the standard (conditional) VAE approach [21, 54]: given a query seed x , sample z from the prior, then forward through the decoder to get approximated samples from p ψ ( x ′ | x,z ) .

Matched flow matching (mFM). We use a continuous normalizing flow [55] to generate samples from the improved conditional distribution by, given an initial seed, (i) first sample from an (easy) source distribution p 0 , (ii) then transform it into a sample from the desired target distribution p + ( x ′ | x ) by solving an ODE.

Until recently, continuous normalizing flows have been trained by directly optimizing the maximum likelihood objective of Theorem 1. However, recently practitioners have switched to the flow matching objective as it allows simulation-free training and tends to produce higher likelihood in practice [22, 56, 57]. In flow matching, one uses a time-dependent velocity field v θ t ( x ′ t , x ) , with t ∈ [0 , 1] , and x ′ t an intermediate sample from the probability path p t ( x ′ t | x ) that defines the velocity

field. We follow [22] and choose the linear probability path. The velocity field is learned by adapting the conditional flow matching loss [22]-that matches the parameterized velocity to the optimal velocity that transports p 0 to p + ( ·| x ) -to our setting:

where x ′ t =(1 -t ) x ′ 0 + tx ′ . In case data is discrete, we can equivalently use the discrete flow matching loss [58, 59]. We sample improved designs by solving the ODE ˙ x ′ t = v θ t ( x ′ t ,x ) , where x ′ 0 ∼ p 0 and x ′ 1 is an (approximate) sample from p + ( x ′ | x ) .

Matched walk-jump sampling (mWJS). Walk-jump sampling [23] is a score-based generative model that approximate samples from p + ( x ′ | x ) byfollowingatwo-stepprocedure, given a (usually high) noise level σ : (i) sample from the smooth distribution p ( y | x )= p + ( x ′ | x ) ⋆ N (0 ,σ 2 I d ) , (ii) then estimate samples ˆ x = E ( x | y ) . Weapproximate the score function with conditional denoiser D θ : R d × R d → R d , a neural network parameterized by θ , that takes as input pairs ( y,x ) and outputs an estimated clean version of x ′ (the clean version of the noisy design). The denoiser is trained by minimizing the following loss:

Following learning the conditional denoiser, we approximate the score function p ( y | x ) using the conditional version of Tweedie-Miyasawa formula [60, Proposition 1], i.e.,

We then leverage the (learned) conditional denoiser ( D θ ) and the score function ( s θ ) to generate designs ( x ′ ) conditioned on seeds ( x ):

(i) (init.) pick an initial seed x and initialize y 0 with noise.

(ii) (walk) sample y k ∼ p ( y | x ) with Langevin MCMC with discretization step δ 4 :

(iii) (jump) generate clean designs at arbitrary step K : x ′ K ← D θ ( y K ,x ) .

Note that the least-squares loss (6) does not correspond to maximum likelihood; however, samples from this model are approximate draws from p + ( x ′ | x ) . The degree of this approximation is controlled by σ [62]. In practice, σ plays the role of a regularizer, both for learning a smoother density and for easing the problem of sampling. Due to the simplicity of this scheme ( σ is the main hyperparameter), it has proven to be an effective sampling strategy in practical applications [63, 30, 60, 64].

3.3 Iterative sampling

Our matched generative models sample designs, given seeds, with improved property and satisfying constraints C ( x,x ′ ) . They are amenable to iterative optimization and, in practice, we apply the sampling procedure multiple times, (implicitly) guiding designs toward higher property values, until some criterion is reached (e.g., the number of iteration, a certain value on the property). Similar to [19], and unlike e.g. [12, 14], our iterative optimization approach does not rely on any auxiliary discriminative models. Unlike [19], the matched models generate a population of designs at each iteration. We propose a simple iterative process: x ′ k +1 ∼ p + ( ·| x ′ k ) , where x ′ k is an element of design set D k and k =0 , 1 ,...,K . Starting from a set of seeds D 0 = { x i } N i =1 (including the case of a single seed), we get a population of improved designs D 1 after the first iteration, which are then used as seeds on the following iteration and the process is repeated. The samples on iteration k +1 should have a better property than the samples on iteration k , while still satisfying additional constraints. Algorithm 1 in appendix describes a simple pseudo-code for this procedure.

3.4 Iterative training on self-generated data

Starting from a small set of N 0 true matched data points M 0 = { ( x 0 ,x ′ 0 ) i } N 0 i =1 , for every step k the model generates new samples optimized for desired properties and pairs them with their original inputs to form pseudo-matched examples { ( x k , x ′ k ) i } N k i =1 . These synthetic matches are then merged back into the training set, M k ← M k -1 ∪{ ( x k ,x ′ k ) i } N k i =1 , effectively enlarging the dataset. This iterative cycle-generate, match, retrain-enables the model to (i) refine its improved target distribution and (ii) explore regions

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of data space beyond the original manifold. As a result, generative performance steadily improves: the model learns from its own best guesses, sharpens its ability to produce high-value samples, and is able to extrapolate property values than could not have been achieved with the initial, limited ground-truth set alone. This procedure is summarized in Figure 3 and Algorithm 2.

Our approach draws from classic semi-supervised pseudo-labeling methods [65, 66] and their modern successors in generative contexts like FixMatch [67], where models reuse their own predictions for training models for supervised tasks. While recent studies highlight failure modes in high-capacity large language models-regression to overly common patterns and failure to explore richer outputs [68, 69]-our work contrasts by focusing on sparse, low-data settings (e.g. early-stage drug or antibody design). Here, we use iterative pseudo-matching to bootstrap new data pairs, mitigate regression to the mean, and push property values beyond the original training manifold, crucially operating without the oracles or pruning methods prevalent in many LLM-based model collapse solutions.

4 Experimental results

Weevaluate the effectiveness of our models on two in silico offline (non-sequential) settings related to protein design. First, we compare our model examples with baselines on a protein fitness optimization benchmark, focusing on subdomains of AAV and GFP proteins (Section 4.1). Then, we show how iterative training on self-generated data can push the boundaries of the designs' properties beyond their scope in the training set (Section 4.2). We emphasize our approach is general and can be applied in modalities other than biological sequences, illustrated on a MNIST toy task presented in Appendix F.

4.1 Protein fitness optimization

Datasets. Weevaluate the performance of our model on two important protein subdomain datasets: adeno-associated virus ( AAV ) [70] and green fluorescent protein ( GFP ) [71]. The former measures the ability of the AA V to package a DNA payload, for applications in e.g. gene delivery, while the latter's fitness is its fluorescence properties, useful for e.g. biomarkers. AA V and GFP datasets contain 44,156 and 56,806 pairs of amino acid sequences and experimentally measured property, respectively.

Weuse the benchmark proposed by Kirjner et al. [14], which contains functional segments of length L =28 and L =237 amino acids for AAV and GFP, respectively. Following common practice, the protein sequences are one-hot encoded over a dictionary of 20 amino acids. The optimal fitness set for each dataset is defined as the top 99th percentile of experimental data with the highest measured property. We consider the two splits proposed by the authors-'medium' and 'hard' splits-with 2,139/3,448 samples for AAV and 2,828/2,426 for GFP. The medium split is a subset of the data containing the 20th-40th percentiles that are 6 edit distances or more from any sample in the optimal fitness set. The hard split contains the lowest 30th percentiles that are 7 mutations or more away from the optimal fitness set. Similar to [19], we consider the following constraints when creating the matched datasets for our models: C ( x,x ′ ) = dist ( x,x ′ ) < ∆ x ∧ ( g ( x ′ ) -g ( x ) < ∆ g ) , where we consider Levenshtein distance, ∆ x of 5 and 10 and ∆ g of .2 and .05 (before normalization) for AA V and GFP tasks, respectively. These thresholds were selected based on an ablation conducted with one model variant, mWJS, on the medium splits (see Appendix C.2).

Baselines. Wecompare our GPE models proposed in the previous section with a variety of methods in the offline optimization setting 5 : GFlowNets (GFN-AL) [72], model-based adaptive sampling

(CbAS)[7], greedy search (AdaLead) [8], a simple Bayesian optimization baseline (BO-qei) [73] (using the implementation of [51]), conservative model-based optimization (CoMs) [9], proximal exploration (PEX) [28], Gibbs with gradients [40] (GWG) adaptation from [14] and its labeled-smoothed version (GGS) [14]. We emphasize that, unlike our models, all baselines rely on a discriminative model either as part of the sampling process or as a way to select designs at each iteration.

Evaluation and metrics. Following [72, 14], each method starts the optimization process with 128 seeds, X = { x i } , and generates 128 designs, X ′ = { x ′ i } , ideally with higher fitness than the initial seeds. For our experiments, we used the top 128 seeds from each dataset, but as shown in the Appendix C.3, our method is robust and performs well regardless of the initial seed selection.

̸

The fitness of generated designs are approximated with a fitness predictor, ˆ g . We use the fitness predictor (and model weights) from [14]. This (pseudo-)oracle is a 1D convnet trained on all wet-lab data provided by [70, 71] and used only for evaluation 6 . The fitness is min-max normalized on all tasks. For fair comparison with previous work, we use the same metrics as in [14] 7 . Given the set of generated designs, we compute: Fitness =median( { ˆ g ( x ′ i ) | x ′ ∈ X ′ } ) , the median of the approximated fitness predicted by the pseudo-oracle (higher is better), Diversity =median( { dist( x, ˜ x ) | x, ˜ x ∈ X ′ ,x =˜ x } ) , the median of the Levenshtein distance between every pair of sequence on the generated set, and Novelty =median( { η ( x ′ i ,X ) } 128 i =1 )) , where η ( x,X )=min( { dist( x, ˜ x ) | ˜ x ∈ X,x =˜ x } ) is the minimum distance of sample x to any starting seed in X . Weare interested in designs that have higher fitness, while diversity and novelty are shown to assess exploration/exploitation tradeoffs. As pointed by [14], random sequences would provide very high diversity and novelty and unreliable (predicted) fitness.

̸

Implementation details. For the iterative sampling, we start with 128 seeds from the training set (similar to other baselines) and sample designs according to Algorithm 1 for K =20 iterations. At each iteration, we sample a pool of M =2560 designs and reject the repeated ones and those that have a Levenshtein distance larger than 10 from any seed. On the final iteration, we randomly pick 128 samples from the last pool of designs. For details on the architecture, training and sampling hyperparameters of our models, see Appendix B.3.

Results. Table 1 and Table 2 compare our matched generative models with baselines on both splits of AAVandGFPdatasets, respectively. Our matched generative models achieve similar or better results than baselines on most tasks, while being conceptually simpler and without relying on any external predictor. We remark that the main contribution of the best performing baseline (GSS), i.e. graph-based smoothing of the fitness landscape, is orthogonal to our approach and could potentially be integrated to our matched models to further improve results.

Figure 4 compares one of our proposed models, mWJS, to its unmatched counterparts, akin to a simplified version of [30]. The two models have the same architecture and hyperparameters, the only difference being that the former is conditioned on the matched dataset while the latter is an unconditional model. It clearly illustrates the benefits of our approach: the median fitness of designs generated by the matched model increases as we do more sampling iterations (until it plateaus), while the fitness of the unmatched one remains mostly unchanged. Table 3 and Table 4 (appendix) shows how the matched version of the generative models improve over the unconditional version for the generative models considered. Finally, Figure 8 (appendix) shows quantitative examples of how the distribution changes over iterations starting from randomly chosen single seeds (not seen during training).

4.2 Iterative training on self-generated data

Dataset. In this task, we focus on optimizing therapeutic proteins-specifically, antibodies-using the mutagenesis library introduced in [74]. This dataset covers three different antigen targets; here, we concentrate on the HER2 subset 8 . Physicochemical properties such as hydrophobicity and electrostatic charge strongly influence a molecule's developability profile, impacting key attributes like viscosity and specificity [75]. Unlike binding affinity or expression, which lack reliable computational proxies, these physicochemical features can be estimated in silico via closed-form metrics that correlate well with experimental measurements. For clarity, we use charge at given pH of a protein to illustrate the

benefits of self-training with exact evaluation. Each antibody is represented in AHo numbering format [76], yielding one-hot encoded sequences of length 298. From the original training set, we randomly select 1,000 examples to mirror the low-data regimes common in real-world drug discovery-often on the order of only a few hundred samples. We use ∆ x =10 and ∆ g =0 . 05 for matching constraints.

Metrics. Weevaluate the performance in terms of per-design metrics: average improvement (AI), the difference in property value between each design and its corresponding seed, and ratio of improvement (RI), the proportion of designs which have improved property values compared to their seeds.

Implementation details. Our architecture and training procedures follow Tagasovska et al. [19]. The overall pipeline is illustrated in Figure 3. At round k =1 , we train GPE models on the dataset of true matched points, generated from N 0 =400 sequences, and evaluate on a held-out test set of 100 examples. Then, for each round k (for a total of K = 4 rounds), we sample new designs, generate new pseudo-match pairs, update the training set and retrain the models.

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Results. Figure 5 demonstrates that across three GPE variants, when starting from only 400 seed sequences, each successive self-training iteration outperforms a baseline trained on 1,000 true examples, both in the fraction of improved designs and in average property gain. Moreover, with each round, the property ceiling rises until it plateaus around round 4, consistent with our limited initial dataset. These results underscore the power of iterative self-training in low-data regimes typical of drug discovery. Appendix D.1 shows an ablation comparing our method with a version where designs for each round are selected using a (trained) predictor or the ground-truth oracle.

5 Conclusion

Weintroduced generative property enhancer (GPE), a novel approach for guiding generative models that circumvents the need for explicit discriminative models, which are often unreliable in low-data regimes and for tail-end distribution properties. GPE offers a simple, scalable, end-to-end, and broadly adaptable solution compatible with diverse generative models and data representations. GPE achieves competitive performance in a standard offline (non-sequential) protein fitness optimization benchmark and can be iteratively trained on self-generated data, successfully applied to an antibody property optimization task.

Our work shares similar limitations to related approaches. First, GPE currently focuses on singleproperty enhancement, which may not fully meet industry expectations for designs that must simultaneously adhere to multiple properties of interest. Second, our current validation has thus far been conducted on in silico benchmarks. Finally, the iterative sampling process involves some hyperparameter tuning (e.g., number of iteration steps, number of seeds per step). We observed, however, that these hyperparameters are transferable between the protein tasks studied, suggesting some degree of robustness. Future work will focus on extending our framework to multiple-property optimization, leveraging domain-specific knowledge for targeted applications, and experimenting with multi-modal representations.

Broader Impact

Design optimization is an important problem in many scientific applications, such as protein engineering, synthetic biology, materials, environment and molecule design. These are very long and challenging endeavors that involve many steps to achieve success. In this paper we propose an approach to this problem, which deals with one of these steps. There is still a lot of work that needs to be done to validate these kinds of models in practice (e.g., lab experimental validation, clinical trials, technological advances, etc). That being said, if successful, advances in this field can directly impact quality of human life. Like many other powerful technologies, we need to ensure that these models are deployed in ways that are safe, ethical, accountable and exclusively beneficial to society.

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Appendix

A 2Dtoy task

Here, we analyze the behavior of one of our models-the matched walk-jump sampling-on a simple task in 2 dimensions. We start with a dataset of 186 points whose property value increases as the points move counter clockwise on the spiral. We then create the matched dataset considering a threshold ∆ x =0 . 5 , ∆ y =0 . 01 and the Euclidean distance between points, with a total of 498 pairs (we use 401 for training). Figure 6 shows the initial and the matched dataset. We proceed by training a mWJS (we use a simple 2 layers MLP as the denoiser) on the matched dataset and use this model to sample new points with (hopefully) increased properties.

(a) Initial dataset

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Figure 7 shows examples of generated designs following our iterative sampling over 50 optimization iterations, starting from unseen test points. We observe exactly what we would expect: (i) the generated samples remain on the manifold of data, (ii) the property of the samples increase as we sample for more iterations, and (iii) samples at each iteration are diverse.

(a) Initial dataset

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B Implementation details

B.1 Iterative sampling algorithm

See Algorithm 1.

B.2 Iterative training on self-generated data

Algorithm 2: Iterative training on self-generated data

B.3 Matched generative models implementation details

The models on this paper were trained using single A100 Nvidia GPUs and 4 CPU workers per model. Training of different models varies, but they all were trained on less than 1 day. The hyperparameters for training and sampling are the same for all tasks, unless stated differently. They were chosen using a subset of the AAV hard task.

mVAE. Weuse the ResNet architecture proposed in [19], which has shown to be an efficient encoderdecoder framework for protein design. We extend this to a matched version by implementing a conditional VAE, with the conditioning on x being concatenated to z the latent representation. We have one layer of one-hot encoding, followed by 3-layer MLP resnet blocks with internal layers of size 128. Each mVAE was trained with Adam, learning rate 1e -4 for AAV and antibodies, and, 1e -5 for GFP, and train for 500 epochs each.

mWJS. Similar to [30], we model amino acid sequences (both seeds and designs) as one-hot encoding lying on the continuous space of dimension d =20 × L . Wechoseanoise level σ = . 5 and generate noisy samples by adding gaussian noise to designs, i.e., y = x ′ + σε , ε ∼ N (0 ,I d ) . Weadapt the architecture of the condition denoiser used for conditional walk-jump sampling from [60] to our setting, i.e., we modify their architecture to be applied to 1D sequences instead of 3D voxel grids. First we pad the two inputs (noisy design y and clean seed x ) so that they have lengths divisible by 8 (required for the denoiser) so that L =32for AAVdataset, and 240 for GFP. The padded inputs are then forwarded through a single 1D conv (with kernel size 1) and added together (or we just encode y in the unconditional setting). The resulting embedding is then forwarded through a 1D U-Net. Here, we adapt the 2D unet proposed by [77] to our 1D setting 9 . Weremove the noise-conditioning, as our denoiser is trained on a single noise level. The architecture starts with 32 and contains 4 resolution levels, each level containing 4 residual blocks. At each resolution level, we downsample (upsample in the case of decoder) the sequence embedding by two while doubling (halving for the decoder) the number of channels. The two last layers of the encoder (two first layers of the decoder) contain self-attention blocks, similar to [77]. The denoiser model has a total of 3.8M parameters, and it is trained with batch size of 256, learning rate 1e -3 , Adam [78] optimizer and a total of 5,000/1,000 epochs for AA V and GFP, respectively.

Sampling is done following the conditional walk-jump sampling from [60] (see Algorithm 1 in the paper). We use underdamped Langevin MCMC with the discretization scheme proposed by [61] with step size δ = σ/ 2 and set γ =1 /δ . Each iteration consists of two walk steps followed by a jump step, which approximates improved designs. The chains in the first iteration are initialized with a seed from the initial set of seeds and uniform + gaussian noise, ( x,y 0 ) , where y 0 = U I d (0 , 1)+ N (0 ,σ 2 I d ) . Each iteration consists of 2 walk steps followed by a jump step, which generates the new sets of design for iteration i . Weuse the designs generated at iteration i to condition the chains on iteration i +1 , until we reach 20 iterations. Note that we do not re-initialize the noisy seeds y at each iteration: they keep being updated as the MCMC chain progresses.

mFM. Similar as above, we use the same data representation and the unet architecture of [77] adapted to the 1D setting. The conditioning mechanism is identical to the original implementation: at each scale we integrate embeddings for the time t and seed x (instead of the class label, as in the original architecture). As we represent molecules as discrete data, we use the discrete flow matching [58, 59] variant. In preliminary experiments, we observed the uniform source distribution p 0 achieved better performance than the masked distribution (where all tokens are masked). We use the implementation from [57] 10 , and in particular, their proposed MixtureDiscreteProbPath path with PolynomialConvexScheduler scheduler ( n =2 ) and the MixturePathGeneralizedKL loss. We also use their provided ODE solver with 32 steps ( ConditionalMixtureDiscreteEulerSolver ). Similar to the mWJS variant, we train for 5,000/1,000 epochs for AAV and GFP, respectively, we use the learning rate of 1e -3 , Adam optimizer and batch size 256.

C Additional results on protein fitness

C.1 Ablation study: Comparison between unconditional models and matched generative models

Table 3 and Table 4 below show empirically the advantage of our proposed method. In this experiment, the architecture and training/sampling hyperparameters are the same for both the unconditional and the matched models (the only difference being the matched conditioning on the latter).

C.2 Ablation study: influence of the constraint criterion

Table 5 shows ablation studies on the ∆ x constraint (Levenshtein distance) for the mWJS model on AAV medium task. We observe that fitness remains relatively stable with lower ∆ x thresholds (0.50-0.53 for ∆ x in 1-7), peaking at 0.53 for ∆ x values of 4, 5, and 6. As ∆ x increases beyond 7, fitness notably declines, reaching 0.45 at ∆ x =10. Diversity generally increases with ∆ x , while novelty shows minor fluctuations. These results indicate that a moderate range for ∆ x (e.g., 4-7) yields optimal or near-optimal fitness. Very small thresholds likely overly restrict generation, while very large thresholds may dilute meaningful local relationships.

C.3 Ablation study: choice of initial seeds

In our main experiments, we start the iterative sampling with the top 128 seeds in the train set. Table 7 compares performance of the mWJS variant when selecting when starting with the top seeds versus randomly choosing the initial seeds (independent of their property value).

Weobserve that the performance across all metrics (fitness, diversity, and novelty) remains consistent, regardless of whether fixed or random seeds are used. The slight variations observed are well within the reported standard deviations, confirming the stability of the results.

C.4 Protein fitness vs number of iterations plots

Figure 8 shows plots of protein fitness improvement vs. number of iterations starting with different initial seeds and generating 200 designs per iteration.

D Additional results on iterative training on self-generated data

D.1 Ablation study

We performed an additional ablation, comparing our original GPE method to a version where the selected designs for each round are conditioned on a discriminator.

Experimental Setup. Wetrained an ensemble of 15 discriminators, each sharing the mVAE encoder architecture with an added classification head. These discriminators were trained to predict improvement labels, I ( x,x ′ ) . We used the charge at pH7 property for consistency with section 4.2. In our first baseline (GPE + Discriminator), we filtered GPE-generated designs, x ′ , using the mean predicted probability from the ensemble and retaining only designs with low prediction variance ( < 0 . 05 ). For an upper bound on performance, we also created a second baseline (GPE + Oracle) where we filtered generated designs using the ground-truth oracle.

Results. Our findings in Table 8 show that the discriminator-based filtering scheme did not improve performance. In fact, it underperformed our original GPE method, while the oracle-filtered version achieved a slight early-round improvement. In the table below, RI and AI are the 'Ratio of Improvement' and 'Average Improvement'.

Weattribute the discriminator's poor performance to domain shift. The discriminator was trained on ( x,x ′ ) pairs with at most two Levenshtein edits, matching the constraints used to build the training set. However, GPE-generated pairs in later rounds span one to ten edits, making them out-of-distribution for the discriminator. This is reflected in the metrics presented in Table 9.

D.2 Diversity analysis

Not all seeds are equal. For some which have more neighbors, i.e. lie in a more dense region in the training data, the model has better chances of learning the implicit direction of improvement and therefore more opportunity for generating diverse candidate designs. Hence, the number of pairs around each seed at round 0, is indicative of the opportunities of improvement.

In Table 10, we notice the expected trend, that is, at each round the number of designs (diversity) per seed goes down both in terms of mean and standard deviation.

E Wet-lab validation

As additional empirical evidence we provide a summary of wet-lab experiments comparing GPE (mPropEn variant) against unconditional WJS [30] for improving therapeutic protein binding affinity across eight initial seeds over three distinct targets as presented in [17]. Our model demonstrates significantly higher and more consistent binding rates (94.6% vs. 62.2%) and design improvements (34.4% vs. 4.8%). Additional experiments benchmarking mVAE vs mPropEn are in progress and will be added to the manuscript as soon as available.

F Qualitative results on rotating MNIST with mWJS

To showcase that our model also works for continuous representation, we test our model on a simple task derived from MNIST dataset. In this toy task, we artificially create a property by rotating digits clockwise. The matched dataset is defined such that for each digit in the dataset, we apply two rotations and give the highest property to the digit rotated with highest angle, i.e., given two random angles θ 1 and θ 2 s.t. θ 1 -θ 2 < 30 ◦ and θ 1 >θ 2 , then g ( R ( x,θ 1 )) >g ( R ( x,θ 2 )) .

Wetrain a matched walk-jump sampling model (using a tiny unet model as denoiser) on this dataset and observe qualitatively what we would expect: starting from an unseen digit, the model samples digits are increasingly rotated clockwise (that is, with higher property).

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces Generative Property Enhancer (GPE), a framework that casts low-data design optimization as an implicit conditional generation task by building matched pairs of low-property and higher-property samples and training a single conditional generative model to reproduce the improved distribution—proven theoretically via paired log-likelihood to recover the optimal conditional density. GPE is instantiated across four off-the-shelf generative paradigms (PropEn, VAE, continuous normalizing flows, and walk-jump sampling) without any external predictor, and it achieves competitive or superior performance on standard protein fitness benchmarks (AAV and GFP) in terms of predicted fitness, diversity, and novelty. Moreover, an iterative self-training loop that re-pairs model-generated high-property samples with their seeds enables the model to extrapolate beyond its original training range, demonstrating strong effectiveness in very low-data regimes.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1.\tEnd-to-end simplicity: GPE trains a single generator to turn raw examples into improved designs, doing away with separate scoring or selection modules.\n2.\tHigh data efficiency: By pairing lower-value examples with higher-value ones and retraining on its own synthetic matches, GPE amplifies scarce data and learns property improvements even from few samples.\n3.\tArchitecture agnostic: GPE slots into any off-the-shelf generative framework, so existing model architectures can be reused for optimization without redesign.\n\nWeaknesses:\n1.\tLimited real-world validation: All experiments are in silico; no in vitro or in vivo experiments are presented, so it remains to be seen how GPE performs under real experimental noise or lab constraints.\n2.\tSingle-property scope: The framework is demonstrated only on single-objective optimization; many practical applications require balancing multiple properties (e.g., activity vs. toxicity), and multi-objective extensions are not explored.\n\nQUESTIONS:\n1.\tI’m not an expert in design optimization—sorry if this is a basic question—but I understand diffusion architectures have become a leading paradigm for high-fidelity sample generation. Have you explored applying GPE within a diffusion framework, or do you anticipate any challenges or necessary adaptations?\n2.\tIn multi-objective design, requiring simultaneous improvements on several properties may reduce the number of valid matched pairs. Have you considered this sparsity challenge?\n3.\tCould you share any insights or guidelines on how sensitive GPE is to choices like the number of iterations?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-22"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a discriminator-free framework for learning conditional generative models for offline (one-round) optimization, primarily of sequences (though it can be applied to continuous domains). Specifically, it is a framework for learning generative models that “mutate” or manipulate existing designs, $x$ such that the resulting designs, $x’$ display improved properties of interest, $g(x’) > g(x)$. The framework can be applied to some of the most popular generative models, such as VAEs and flow matching.\n\nThe focus of this work is on directly learning new conditional generative models, as opposed to guiding samples (designs) from pre-trained models, or fine-tuning pre-trained models.\n\nThe key contribution of this work is in formulating a simple yet empirically effective matched-maximum likelihood training framework than can be applied to many generative models.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- The paper clearly presents a relatively simple, intuitive maximum likelihood framework, which is empirically compelling, besting many much more complex methods. This could be a somewhat controversial work, and I think should be of interest to the community.\n- The method can be applied to condition many existing generative models for offline optimization tasks, and so is potentially significant.\n- The exposition is mostly clear and easy to follow, and the losses etc are well justified.\n- The method is compared to many existing baselines on established benchmarks.\n\nWeaknesses:\n- Missing complete problem setting description, i.e. this is for offline sequence optimization (one-round of experimental validation, with no feedback), and not online optimization. However, much of the related literature also misses this point. It may also be worth clarifying that this is not for guidance of pre-trained models [Ho, 2022; Ye 2024], which is also a large topic in this space.\n- Missing ablation studies or intuition behind of some design choices. I.e. (1) the influence of the constraint criterion, $C(x, x’)$, in the model’s generative performance, and the importance and function of the choice of this criterion (distance metric and threshold, $\\Delta_x$). E.g., how important is using this term to prevent “out-of-domain” generation (related to [Klarner, 2024]), and how does it interact with the iterative self training strategy? (2) One could imagine training a classifier, $p(z|x, x’)$, where $z = I(x, x’)$ or even a regressor $z = g(x’) - g(x)$, resulting in $p(x’| z, x)$ thereby still using a discriminator, but also increasing the dataset size. How does this compare to the no discriminator setting as both methods now have access to the same data (that is, how much performance results from the increased data, vs. discriminator)?\n- The AAV and GFP experimental datasets use machine learning oracles, which have known deficiencies (overfitting), potentially making these problems unrealistic [Surana, 2024]. It is worth pointing out these limitations in the text. I like the addition of the anitbodies experiment. Maybe you can also consider the Ehrlich closed-form test functions of [Stanton, 2024], also implemented here: [poli](https://machinelearninglifescience.github.io/poli-docs/using_poli/objective_repository/ehrlich_functions.html), and/or the simple but combinatorially complete datasets (DHFR, TrpB) used by [Steinberg, 2025] to augment these results with oracle free experiments?\n\nOverall I find this paper fascinating, and a very promising direction. I feel like it needs a little more clarification of the problem it is solving, e.g. it is not for guiding pre-trained models, or for online optimization etc. I think it needs at least some ablation studies to justify the design choices and settings, e.g. how sensitive is it to $C(x, x’)$ and $\\Delta_x$. Also, I question (some of) the discriminator-free claims, when a discriminator-based model ($p(z|x, x’)$ and $z = I(x, x’)$) solving a similar improvement objective, _with similar training data_, may also perform as well (or maybe better). I do really like the simplicity and modularity of the framework though.\n\n[Klarner, 2024] Klarner, L., Rudner, T.G., Morris, G.M., Deane, C.M. and Teh, Y.W. Context-guided diffusion for out-of-distribution molecular and protein design. The 41st International Conference on Machine Learning (ICML 2024), 2024.\n\n[Steinberg, 2025] Steinberg, D., Dos Santos De Oliveira, R., Ong, C.S., Bonilla Pabon, E. Variational Search Distributions. International Conference on Learning Representations (ICLR 2025), 2025.\n\n[Surana, 2024] Shikha Surana, Nathan Grinsztajn, Timothy Atkinson, Paul Duckworth, and Thomas D Barrett. Overconfident oracles: Limitations of in silico sequence design benchmarking. In ICML 2024 AI for Science Workshop, 2024\n\n[Stanton, 2024] Stanton, S., Alberstein, R., Frey, N., Watkins, A. and Cho, K., 2024. Closed-form test functions for biophysical sequence optimization algorithms. arXiv preprint arXiv:2407.00236.\n\n[Ye, 2024] Ye, H., Lin, H., Han, J., Xu, M., Liu, S., Liang, Y., Ma, J., Zou, J.Y. and Ermon, S., 2024. Tfg: Unified training-free guidance for diffusion models. Advances in Neural Information Processing Systems, 37, pp.22370-22417.\n\n[Ho, 2022] Ho, J. and Salimans, T., 2022. Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598.\n\nQUESTIONS:\nQuestions:\n- Do you think the empirical performance of this method is from the increased training set size and (discriminator free) implicit improvement objective? Or do you think we could also achieve as good performance with a discriminator explicitly trained on labels $z = I(x, x’)$, which would also have access to a large dataset (or larger, since we have negative labels)? Do you think there would be less need for iterative self training using a trained guide of this form? I understand the benefit of the increased dataset size as a result of using this improvement objective, but I’m unsure about the tradeoff between discriminator based vs. direct conditioning (discriminator free) given the requirement of iterative self training in the discriminator free setting (though I do like the simplicity of the discriminator free model).\n- Why use the notation $y$ in the Lagrangian, is there an issue with just using $x$? If you want to use $y$, it should also be defined, e.g. space membership, etc.\n- How does this work relate to preference learning, and direct preference optimization (DPO) [Rafailov, 2023] — I feel like there is a deeper connection here to this literature that is perhaps missed, and could be important to contrast to ($x$ could be the context/prompt, $x’$ the response, then how does DPO differ?). \n- This is a slightly tangential question, but it may be worth considering. In online black box optimization tasks (Bayesian optimization/multiple rounds), a discriminator allows us to model the expected utility of measuring a design, $E_p(g|x)[u(g)]$. E.g. in [Steinberg, 2025; Brooks, 2019] this is probability of improvement, $u(g) = I[g(x) > \\tau]$, and in [Gruver 2023; Stanton, 2022] this is expected hypervolume improvement (EHVI), or expected improvement (EI) for one objective, $u(g) = max(g(x) - \\tau, 0)$, for some incumbent or threshold $\\tau$. These acquisition functions allow us to explicitly trade-off exploration of uncertain parts of the design space, vs. exploiting known good areas. It would be very interesting to know if your improvement criterion implicitly matches existing acquisition functions (e.g. knowledge gradient, or some local variant), and has an implicit exploration/exploitation tradeoff -- though I also understand that for offline optimisation tasks, we are more interested in exploitation (modulo diverse batch-design concerns).\n\nComments/Suggestions:\n- I strongly suggest including ablation studies in the final work, as mentioned in the “strengths and weaknesses” section.\n- Better situate your work in the wider body of literature, e.g. online sequence optimization, guided generation (guided diffusion/flow matching), preference learning and alignment (e.g. DPO). \n- Clarify your focus is on offline optimization, or compare to online benchmarks with baselines [Stanton 2022; Gruver, 2023; Steinberg 2025; etc].\n- It is a little odd that the formulation is for $x \\in R^D$ where the applications mainly focus on designing sequences, $x \\in V^D$, where $V \\in \\\\{0, \\ldots, A\\\\}$ for some vocabulary/alphabet size A. Perhaps it is worth presenting this slightly more generally, or saying that the presentation in  $R^D$ is for clarity, but the generalisation to sequences is straightforward.\n- It may be worth clarifying that Z in eqn. 1. is intractable to compute (being a high dimensional CDF), and that is why eqn. 1 is not solved directly. For the case where x is a sequence, this could be a summation over a combinatorial number of elements.\n\n[Rafailov, 2023] Rafailov, R., Sharma, A., Mitchell, E., Manning, C.D., Ermon, S. and Finn, C., 2023. Direct preference optimization: Your language model is secretly a reward model. Advances in Neural Information Processing Systems, 36, pp.53728-53741.\n\nLIMITATIONS:\nThe limitations are adequately addressed, once the focus on offline optimization etc. is clarified.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-23"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper considers the problem of data-driven design optimization, aiming to generate new designs with improved properties over existing ones. The paper presents a method titled Generative Property Enhancer (GPE) where the core idea is to reframe the problem as conditional density estimation. This is achieved by first creating a \"matched dataset\" of pairs (x, x') from the original data, where x' has a higher property value than x. A conditional generative model is then trained on these pairs to directly learn the mapping from a lower-property \"seed\" x to a distribution of higher-property \"designs\" x'. The paper demonstrates how this framework can be applied to various generative model backbones. The framework is evaluated on two in-silico benchmarks.\n\nSTRENGTHS AND WEAKNESSES:\n- The paper considers an important problem of wide real world interest and applicability. \n\n- I think the problem formulation is a bit strawman. The central motivation of the paper is as framed as avoiding discriminative models. The introduction states that \"training a reliable discriminative model is often not feasible\" and that they are \"unreliable at the tail-ends of distributions.\" The paper presents it as a fundamental roadblock that the field has not adequately addressed, which is a bit overstatement. An entire field of Bayesian optimization exists and is dedicated to handling this challenge by incorporating model uncertainty, especially in small-data settings. As it is widely known folk-knowledge now, BO baselines are significantly weaker in a large part of molecule design and protein design literature which always shows them falling behind. Well tuned BO does work and is state of the art method for many of these benchmarks (please see [1] for reference). \n\n  [1] Tripp, Austin, and José Miguel Hernández-Lobato. \"Diagnosing and fixing common problems in Bayesian optimization for molecule design.\" arXiv preprint arXiv:2406.07709 (2024).\n\n\n- The strongest baseline in the paper's own experiments, GGS, explicitly uses a \"smoothed fitness landscape\". Unfortunately, the paper’s current narrative doesn't engage with why these existing solutions are insufficient and instead presents its \"predictor-free\" approach as the necessary paradigm shift. \n\n- Please see and discuss modern Bayesian optimization approaches that work with deep generative models over structured design spaces with small number of samples [2, 3]\n\n  [2] Gruver, Nate, et al. \"Protein design with guided discrete diffusion.\" Advances in neural information processing systems 36 (2023): 12489-12517.\n\n  [3] Maus, Natalie, et al. \"Local latent space bayesian optimization over structured inputs.\" Advances in neural information processing systems 35 (2022): 34505-34518.\n\n- The creation of the matched dataset M depends on crucial constraints C(x, x'), which are controlled by hyperparameters like the Levenshtein distance threshold Δx and the property improvement threshold.  The size and character of M are highly sensitive to these choices. A very strict Δx might yield too few pairs, while a loose one might teach the model to make unrealistic jumps. The paper provides the values used but offers no ablation or sensitivity analysis. Please consider adding a detailed discussion on this aspect. \n\n- The iterative application of GPE, where x_{k+1} ~ q_θ(· | x_k), is a form of stochastic greedy search. At each step, it samples from a distribution of \"locally better\" points. The definition of \"local\" is implicitly learned from the data and heavily influenced by the constraints C(x, x'). Please consider discussing why this would be better than the principled exploration/exploitation tradeoff we get from model uncertainty based optimization procedures like Bayesian optimization.\n\nQUESTIONS:\nPlease see Strengths And Weaknesses section.\n\nLIMITATIONS:\nIt would be great to see some discussion on critical assumptions behind the framework. I believe, for this method to work, the initial dataset D must contain a sufficiently dense set of samples that form a contiguous path from low-property regions to high-property regions.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 1, "ORIGINALITY": 2, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work proposes training conditional generative models on pairs of samples (with one having higher property than the other) in iterative rounds to perform optimization in the design space. The key feature of the proposed method is that it does not rely on surrogate estimates of the property which makes it favorable for low-data regime.\n\nSTRENGTHS AND WEAKNESSES:\nStrength: The proposed method does not rely on the surrogate estimates of the property being optimized. This is an important factor, as in many practical applications, reliable surrogate estimates of the desired property cannot be achieved especially in under explored regions of the design space.\n\nWeakness: lacking theoretical novelty\n\nQUESTIONS:\n1) The matched variants of the presented generative models are simply conditional generative models where generation of x is conditioned on its matching pair with no modification to the formulation of these well-known generative models. Am I missing something?\n\n2) Fix the reference to \"the least squares loss 3.2\" in line 172. What is it referring to?\n\n3) In each training round, how many samples are generated per conditioning seed sequences? Have \nyou performed any ablation on the number of samples generated per seed? Does it have a significant impact?\n\n4) There is a mismatch between M_k defined in subsection 3.4 and Algorithm 2 in Appendix. In the main text M_k is the cumulative set of samples up to round K whereas it is the set of matched sample pairs generated in round K in the Appendix Algorithm 2.\n\n5) It looks like the benchmark has been performed with a fixed set of initial 128 seeds/sequences, \nSo the variability in performance (five runs) is only originated from the model stochasticity. Working with small initial datasets happens a lot in practice as mentioned by this study. I think \nPractically, it is important to assess the model's performance variation with respect to the initial dataset. Also, please provide a justification for fixing the initial dataset (seeds) and this initial set has been generated. \n\n6) (Nice-to-haves) Missed citation for a recent generative-based method [1] addressing important practical challenges of protein design.\n\nReferences:\n[1] Ghaffari et al. Robust Model-Based Optimization for Challenging Fitness Landscapes. ICLR 2024.\nhttps://arxiv.org/pdf/2305.13650.\n\nLIMITATIONS:\nNA", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-12"}