Generative property enhancer:  implicit guided generation through conditional density estimation
Authors: Pedro O. Pinheiro
Pan Kessel
Aya Abdelsalam Ismail
Sai Pooja Mahajan
Kyunghyun Cho
Saeed Saremi
Natasa Tagasovska
Venue: NeurIPS 2025 poster ()
Keywords: generative modeling
drug discovery
design optimization
Primary area: machine_learning_for_sciences
TL;DR: We cast the problem of design optimization as as (implicit) conditional generation, we provide general theoretical guarantees and show its benefits empirically on standard protein engineering benchmarks

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
Pedro O. Pinheiro' Pan Kessel
Aya A. Is Sai Pooja Mahajan
Kyunghyun Cho Saced Saremi!
Nataša Tagasovska'
Prescient Design, Genentech, 2uidd Labs, New York University
Abstract
Generative modeling is increasingly important for data-driven computational design. Conventional approaches pair generative model with 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, coodality-agnosticc and integrates seamlessly with diverse generative model architectures and losses. We demonstrate competitive empirical results on standard in silico offline (nouseeuettiaa)) protein fitness optimization benchmarks. Finally, propose iterative training combination of limited real data and self-generated synthetic data, enabling extrapolation beyond the original property ranges.
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 explore in this work is the problem of design optimiza- tion', where the goal is to produce optimized samples (designs) according to some desired property(ies).
design. An important application- the
Conventional data-driven approaches are usually composed of two modules: (i) 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 reliable discriminative model 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 mechanism proposed by Tagasovska al. [19] and take it 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
"This work was done while the author was at Genentech.
Herre "design optimization" is taken in its broader, applied meaning common in science and engineering, different from its formal mathematical definition.
39th Conference on Neural Information Processing Systems (NeurIPS 2025).

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10
-15
Dataset
(b) Unguided generation (c) Implicit guided optimization (d) Implicit guided generation
Figure 1: (a) An illustrative 2D dataset where the property increases counter clockwise. (b) Uncondi- tional/unguided generative models trained on this data sample diverse points (marked as colored dots) but are unaware of their property values. (c) Implicit guided optimization [19] generates points with eetieggiaatttmmiiaaiin optimization step. (d) Our method able to sample diverse points with increasing values of the property. The colormap indicates the number of iterations. Appendix A further explores this example.
higher properties than the initial seed (marked as cross), where each point is subsequent
the probability density of improved designs. As a result, our framework is more readily applicable to diverse settings, data modalities, and generative models- and it mitigates a core limitation of point- based methods: their tendency converge local maxima [20, Section 4].
Our aaproach-generaatiii property enhancer (GPE)-utiiizes 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 conditional density estimation problem wherein the generative model is compelled-via e.g. maximum likelihood training or approximating conditional score functions- reproduce the distribution of samples with improved properties. Thus, excluding the reliance on any external discriminative model?.
GPE provides an end-to-end, simple and scalable way 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-an generative models and data modalities. Figure 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-sequeml sequentiulll protein fitness optimization two well-studied protein domains (Section 4).. (iv) We show how GPE can "self train", pushing the boundaries of the designs' property beyond their scope 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, 1 11, 25, 15], reinforcement learning [6, 26, 15], genetic seoorith--based approaches [27, 8, 28, 29], energy- based methods [30, 31, 14), methods based on machine translation [32, 33, 12] and ceddictor-guider generative models [34, 7, 13, 35-39]. These approaches 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 generative model to produce design candidates at each iteration.
typically deployed in either offline
"These discriminative models are called by different names, such as, predictor, scorer, surrogate, proxy. (pseudo-Joraal Joracle, etc.

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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 continu- ously 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 certain threshold). Kirjner et al. [14] propose an approach where they iteratively use Gibbs sampling [40], followed by scorer-based selection, smoothed protein fitness landscapes. In contrast previous work, GPE introduces a domain and modality- framework, comes with new theoretical guarantees that
link generated samples to the property improvement. Moreover, unlike previous work, method does not rely on discriminative models on any step of training, sampling or selection. Therefore, can easily be integrated with previous work, potentially improving performance even further.
Our pairing step induces 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 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 conditional diffusion model with direct preference objective for antibody co-design and Mistani et al. [46] uses DPO on curated mhosen-rrjectte 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- guidance [48] approaches, commonly used to guide diffusion models [49, 50] (and some instantiations of flow matching). either by leveraging trained classifier (classifier guidance) or by using the low-property seed as the conditioning signal (classifier-fres guidance).
fact, our framework could seamlessly be integrated into both approaches,
3 Implicit guided generation by data matching
3.1 Problem setting
We address the problem of offline optimization [2], also known as moodel--bseed optimizatin, where the goal to optimize black-box function using only fixed, static dataset. This paradigm stands in contrast 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 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, Rdd or discrete space of length L over a finite vocabulary V (e.g. for proteins |V/ = 20). Let g: + R be a function that quantifies the property of interest. Given a seed x X, our objective is to generate new candidate designs x' E satisfying two conditions: (i) the designs' score must exceed that of the seed, g(x') > (xx), and (ii) the designs must satisfy a set of constraints, represented by a boolean function C(I,xx) ). For example, this function could encode bound on the distance between seed and design, C(I,x') (2.)) < Ag for some threshold Ag R
In this work, we cast the problem above a conditional generation problem, i.c., learn how to sample from the improved distribution given an initial seed x::
p (<'1<)) = ((=')( Z(x)=
D / 100=fooa')(ezz0 p(a'))(z,z''ddd
(1)
Z(x)
where the indicator I((x,x') is given by:
T(,,0r) 1, g(x')>9(<) A((xx'),
0, otherwise.
3

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The normalizing factor (x)) in (1) is generally intractable due to the (usually) high dimensionality of the data and cannot be solved directly. The following theorem establishes learning criterion for the improved distribution.
Theorem 1 (Optimality of implicit property enhancement). Let p(x) be probability distribution and pt (d)))) its corresponding improved distribution, as defined in (1). Consider the objective functional:
L(g) = -xz=p(a) (Eeg (<' Dogg(>'
where q( x.) is any family of conditional densities with supp(p*) Cupp("")C supp(g). Then, the objective (g) has the unique minimizer:
Proof. Introduce a Lagrange multiplier Max) for the constraint, (((2 1x)dx'= =1. The Lagrangian is defined as:
-(.A)=-Jun -mma)) maa) /ft(t (1'((x)))oooull (z))logg(a' (x)da' do + f fotel alo' ((o'(=)dd'' - -)de.
Taking the functional derivative w.r.t. g(z (x) and setting it to zero gives:
p(x)p= (o +p(x))(x)=0 =0 (<<1|==)= p (a' xx)
q('1l x))
1(x)
Enforcing normalization f daaa' x)) dx' = forces A(x) = 1. Hence (x' xx) = (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 variational inference and can be easily ensured with appropriate architecture choices. Furthermore, note that the proof is adaptation of similar approach for showing that maximum likelihood recovers the ground truth density at optimality.
A one-dimensional example. To build intuition, consider the following one-dimensional example: The data distribution p(x) is the standard normal and the property interest is defined as g(x) - -(x 11..
For given suboptimal sample y. the improved distribution is defined as pt (a' [y) (xp(2')(((xx)) g(v)). We now try to compute the conditional expectation f' (v) s B [((²)) >> g(v)]. the probability p(g(a') > gv)). and comparison of the quality g(y) to the average quality of improved samples. From Figure 2, we observe few things: (i) Conditional Expectation: When y is far from the optimal region (x Rz 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 s' values but also consistently have enhanced quality g(x") relative g(y).
Conditional Expectation of Improved Samples
Prepablity levervvement
Probability of finding Superior Sample
Property Values: Input vs. Superior Samples
0.8
0.8
Proporty Value
Mol rimproved
0.6
0.4
0.4
0.2
glyl
(yy)= efx' gix)> styl
Piyte) glyl
-14
Mean giX't for superior samples
0.0
0.0
-16
-3
-2
-1 D
-3
-2 -1
1
-3
-1 D
2
y (starting point)
ysstarting point)
(starting point)
Figure 2: Left: Conditional expectation f") E [x' g(2') > ((v) as function of the starting sample y. This panel illustrates that when y is far from the ideal (i.c., lower quality), the expected superior sample x' is significantly higher, indicating large potential for improvement. Center: Probability p(g(=')= > g(y)) of finding superior sample z' increases for lower-quality and decreases as y approaches the optimal quality. Right: Comparison of the original property g with the mean property value of the superior samples E [=g("') g((x)) ((')= > g(y)] reveals that the improved samples indeed possess higher quality.

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3.2 Matched generative models
Given an initial dataset D = {(r, g(2;) Is X, g(x:) E R and set of constraints C(r,x²) X x X (True, False), we construct matched dataset M {(,,), following Tagasovska et al. [19]:
M (xxx:
g(x) (x(x,2))
(2)
where x and x' are elements D. By construction, M contains samples drawn from p (x') (x)p(x) We stress 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 particularly desirable in the low-data regime.
Equipped with Theorem and matched datasets (2), our goal to learn conditional generator qe (z') (z). parameterized by 8, that approximates the improved distribution pxxlzz). This is done by minimizing the following loss:
((OM))=
Σ
(o (x)
(3)
(M
The minimization of ((,, 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 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 approximate the gradient of the property of interest by minimizing matched reconstruction loss, between a sample with low property and its higher-valus 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-likelln likelihood loss in (3). Here we extend the gradient- based PropEn into an instantiation of matched generative models²: we sample set of designs from the logits of the model (by choosing appropriate temperature).
Matched variational auto-encoder VAE). We instantiate qe (a' (x) as a variaale model defined as:
go (z' (x) (x' |x,=)) (=,,,== (z,2))dz,
parameterized by 0= (d) where ai and vb are parameters of the encoder and decoder, respectively. Training is done by minimizing the following negativve ELBO [21, 53]:
(..) =-
Σ Bus(sl (a' |x,2) + (20 [ (x,2))EM
(4)
where N(2;0,Ja) is the standard d-dimensional normal distribution. This objective is a lower bound of the maximum-likelihood likelihood problem in Theorem 1. Hence, the VAE approximates the optimal density while providing tractable latent representation and sampling mechanism. We sample designs following the standard (conditional) VAE approach [21, 54]: given query seed æ, sample from the prior, then forward through the decoder to get approximated samples from p. px (z']z,22)
Matched flow matching (mFM). We use 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 Po. (ii) then transform it into a sample from the desired target distribution p (x'lar 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-freg training and tends to produce higher likelihood in practice [22, 56, 57J. In flow matching, one uses time-dependent velocity field ef (x1,,)) with t e [0,1], and 24 an intermediate sample from the probability path pt (24) (r) that defines the velocity
'We abuse notation by calling this model "matched PropEn". since [19] also leverages matched datasets. The difference is how the model to sample designs.
5

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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 po to top*
topt( (-1zc) to our setting:
LMFM (0,M)
Σ 1, pollo (x( (x' x')1l
(5)
(x,z"))
where z/ = (1--t)x tz'. In case data is discrete, we can equivalently use the discrete flow matching
loss [58, 59]. We sample improved designs by solving the ODE i = of (x), where x6 ~ Po and 4i is an (approximate) sample from pt (ar (z:)..)
Matched walk-jump sampling (m (JS). Walk-jump sampling [23] is a score-based generative model approximaeee samples from p* (a' | by following two-step procedure, given a (usually high) noise level a: (i) sample from the smooth distribution p(y =pp (a'' (z)x>(0,,of1a). (ii) then estimate sam- Rd x Rd RR neural network parameterized by 0, that takes as input pairs (y.a) and outputs an estimated clean version of x (the clean version of the noisy design). The denoiser is trained by minimizing the following loss:
ples -= Rx We approximate the score function with conditional denoiser Do:Ra
LmwJs (0.M) =
Σ Be-N Do (Z,,e))M
Do +o
(6)
Following learning the conditional denoiser, we approximate the score function p(y|z) using the conditional version of Tweedie-Miyysanee formula [60, Proposition i..
Vlog p(y|z) ~ so (Do(v==))))
We then leverage the (learedd) conditional denoiser (Dş) and the score function (sg) to generate designs (x') conditioned on seeds (z):
(i) (init.) ) pick an initial seed and initialize yo with noise.
(ii) (walk) sample yv: ~p(y|a) (r) with Langevin MCMC with discretization step 8*:
yk+1 = yv + 580 2 ex 2 N(O.Ta).
(iii) (jump) generate clean designs at arbitrary step K: x'x + (UKK
Note that the crast-squares loss (6) does not correspond to maximum likelihood; however, samples from this model are approximate draws from p* [x'[z). The degree of this approximation is controlled by [62]. In practice, plays the role of regularizer, both for learning smoother density and for easing the problem of sampling. Due to the simplicity of this scheme (a is the main hyperparameter), has proven 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(xx,2)) z'). 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 reached (e.g., the number of iteration, 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 population of designs each iteration. We propose simple iterative process: T441 p= (-la))) where z'g is an element of design set DR and == O.1..., Starting from set of seeds Do {xr (including the case of a single seed), we get a population of improved designs D2 after the first iteration, which are then used as seeds on the following iteration and the process is repeated. The samples iteration k++1 1 should have better property than the samples on iteration k while still satisfying additional constraints. Algorithm in appendix describes simple pseudo-code for this procedure.
'The kinetic Langevin MCMC [61] has better mixing properties, which we do not discuss here due space.

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3.4 Iterative training on self-generated data
Pieaad AAEI0
Starting from a small set of No true matched data points M, = (2)) No for every step k the model generates new samples optimized for desired properties and pairs them with their original inputs to form pseudo-matcher maached exam- ples {< x ) These synthetic matches are then merged back into the training set, Mr M4-1 ( (zgg,aa) (gg ) effectively enlarging the dataset. This iterative cycle- generate, match, retrain-enables the model to (i) refine its im- proved target distribution and (ii) explore regions 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.
Pretudo
Nodel 2
Legend
Pocuddi
Model
Pratucts
Natched
Hatth Dulia
Matcchdd Ditta 3
Figure 3: Iterative training with pseudo matches.
Our approach draws from classic semi- suniiiiueeeiiedd 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-capaciny large language
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- masuddnttching to bootstrap new data pairs, mitigate regression to the mean, and push property values beyond the original training manifold, crucially operating without the oracles pruning methods prevalent in many LLM- --baseddddd-d model collapse solutions.
4 Experimental results
We evaluate the effectiveness of our models on two in silico offline (non- (ron-sequential) settings related to protein design. First, we compare our model examples with baselines on 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
We evaluate 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 AAV to package DNA payload, for applications in e.g. gene delivery, while the latter's fitness is its fluorescence properties, useful for e.g. biomarkers. AAV and GFP datasets contain 14,156 and 56,806 pairs of amino acid sequences and experimentally measured property, respectively.
Datasets.
We use the benchmark proposed by Kirjner et al. [14]. which contains functional segments of length I= 28 and L= 237 amino acids for AAV and GFP, respectively. Following common practice, the protein sequences
one-hot encoded over 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-"medinnn 2,139/3,444 samples for AAV and 2,828/2,428 for GFP. The medium split is subset of the data containing the 20th-40th percentiles that are 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 [19], we consider the following constraints when creating the matched datasets for our models: C(zxx') = dist(x,x') < Az A (g(x') g(z) < Ag), where we consider Levenshtein distance, AS of and 10 and Ag of and ,05 (before normalization) for AAV 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).
and "hard" sptits-with
Baselines. We compare our GPE models proposed in the previous section with a variety of methods in the offline optimization setting": GFlowNets (GFN-AL) [72], model-based adaptive sampling
'The baseline results taken from [14].
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(CbAS) [7], greedy search (AdaLead) [8], 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 [1 [14] and its
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 way to select designs at each iteration.
Evaluation and metrics. Following [72, 1 14], each method starts the optimization process with 128 seeds, X = }. and generates 128 designs, X" { 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, 9. We use the fitness predictor (and model weights) from [14]. This (pseudo- Joracle is 1D convnet trained on all wet-lab data provided by [70, 71] and used only for evaluation The fitness is min-max normalized on all tasks. For fair comparison with previous work, we use the same metrics as in [14]'. Given the set of generated x }). the median of the approximated fimeess predicted by the pseudo-oracle (higher is better), Diversity= median (z,))( x, E X ,x { the median of the Levenshtein distance between every pair of sequence on the generated set, and Novelly= (ovelyy-median(( [1((2,. x) ((2))) )), where (xx,))) = min = (dist (i,s) X x + is the minimum distance of sample to any starting seed in X. We are interested in designs that have higher fitness, while diversity and novelty are shown to assess exploration/exploitee
designs, we compute: Fimess== (e
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 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 and Table 2 compare our matched generative models with baselines on both splits of AAV and GFP datasets, 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- 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, MIIS to its unmatched counterparts, akin to simplified version of [30]. The two models have the same architecture and hyperparameters, the only difference being that the former 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 self-generated data
Dataset. In this task, we focus on optimizing therapeutic proteins- sppcifically. mutagenesis library introduced in [74). This dataset covers three different antigen targets; here, we concentrate on the HER2 s Physicochemical properties such as hydrophobicity and electrostatic charge strongly influence molecule's is 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 dlosed-form metrics that correlate well with experimental measurements. For clarity, we use charge at given pH of a protein to illustrate the
the
USsing trained models to approximate fitness is obviously unreliable and should be taken with a grain of salt. It does provide, however, a convenient way to compare different methods in toy-task setting.
We use the implementation provided by the authors in https: thit com/kir jiir/nneGGGS. 'Human epidermal growth factor receptor 2, oncogene with an important role in the development and progres- sion of certain aggressive types of breast cancer.
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Medium difficulty
Hard difficulty
Method
Fitness
Diversity
Novelty
Fitmess
Diversity
Novelty
GFN-AL [72]
0.20 (0.1)
(1.2)
19.4 (1.1)
(0.1)
11.6 (1.4)
(1.6(
CbAS [7]
0.43 (0.0)
12.7 (0.7(
7.2 (0.4)
(0.0)
(4.7)
8.5))
AdaLead [8]
0,46 (0.0)
(0.8)
2.8
(..0
8.5
(..5)
BOqei [73]
(0.0)
(0.8)
0.0
(0.0)
(0.9)
0.0
CoMS [9]
0.37 (0.1)
(5.1
(32))
(.26(
(0.7
10.0
PEX [28]
(0.0)
(0.0)
(.2)
(0.0)
(0.0)
(.3)
GWG [40]
0..1(
6.6(6.3)
(.8)
(0.0)
(2.0
12.2
GGS [14]
0.51 (0.0)
(.0.
(0.))
(0.0)
(0.)
7.0)
GPE (ours)
mPropEn
(0.02)
(..7)
(0.7)
0.38 (0.04)
8.7 (0.7)
7.8)
mAE
0.48 (0.02)
9.5
6.00)
0.38 (0.04)
(1.0
(..)
mFM
0.52 (0.01)
6.2 (0.2)
(.6
0.35 (0.02)
(0.3)
(..))
mWJS
0.53 (0.01)
5.2 (0.2)
(..)
0.54 (0.04)
(0.))
(.5)
Table AAV benchmarks results. Results are shown with mean/standard deviation across runs. We bold and underline the best and second best fitness score, respectively. Unlike our models (bottom), all baselines use discriminative model to guide sampling. Details about baselines and metries can be found in Section 4.1.
Medium difficulty
Hard difficulty
Method
Fitness
Diversity
Novelty
Fitness
Diversity
Novelty
GFN-AL
0.09 (0.1)
25.1 (0.5)
213 (2.2)
0.10 (0.2)
23.6
(4.(2
CbAS [7]
0.14
(1.1)
7.2 (0.4)
0.18 (0.0)
9.6().3)
(0.4)
AdaLeea [8]
(0.6)
(0.1)
(.00)
0.18
(.5().5)
(0.4)
BOqei [73]
(0.0)
19.3
0.0
(0.5)
9716
54.1
CoMS [9]
(0.1)
133
192
(.10
(4.5)
201 (3.0)
PEX [28]
(0.0)
3.0
(.42)
(.00
3.0
1..3)
GWG [40]
0.10
(3.8)
12.8
0.00
(7.0)
71.
GGS [14]
(0.0)
(..
(.00)
0.74
(..
8.0
GPE
mPropEn
0.62 (0.02)
40.3).3)
(0.4)
0.88 (0.02)
(0.)
(0.00
mVA
00.03)
1..))
(..7)
0.78 (0.04)
1.3)
(..6)
mFM
0.50 (0.03)
(0.2)
(..0)
0.55 (0.04)
(..1
(0.5)
mWJS
0.76 (0.03)
30.1)
(0.0)
0.78 (0.02)
2.2)
7..)
Table 2: GFP benchmarks results. Results are shown with mean/standard deviation across 5 runs. We bold and underline the best and second best fitness score, respectively. Unlike our models (bottom), all baselines use discriminative model to guide sampling. Details about baselines and metrics can be found in Section 1.
benefits of self-training with exact evaluation. Each antibody represented in AHo numbering format [76). yielding one-hot encoded sequences of length 298. From the original training set, randomly select 1,000 examples to mirror the low-data regimes common real-world drug discovery-one on the order of only a few hundred samples. We use A 10 and A, = 0..05 for matching constraints.
Metrics. We evaluate 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. round
we train GPE models on the dataset of true matched points, generated from No = 400 sequences, and evaluate on held-out test set of 100 examples. Then, for each round (for a total of K =4 rounds), we sample new designs, generate new pseudo-match pairs, update the training set and retrain the models.

---

2.5
(Nomalaad)
Iteration
Terratio
GFP hard
Figure 4: Normalized fitness per iteration (for total 20 iterations) for AAV (a) and GFP (b) hard splits. We show results for WJS (red) and mWJS (blue). The dashed lines correspond to the fitness of training sample with maximum fitness. For each iteration, the median and 25-75 percentiles shown. We start with 128 seeds from training set (iteration 0) and iteratively sample designs for total of 20 iterations.
Average improverenn of tess designs
1.0
2.2
Ratio of improved test designs
2.0
1.8
0.6
1.6
0.4
1.4
0.2
mPropEn niVAE mijjs
1.2
1.0
Round number
Round number
Figure 5: Iterative training with three GPE models starting from only 400 examples. Each panel shows how RI (left) and AI (right) metrics evolve over four rounds. The dashed lines show performance of model trained on 1,000 samples. All methods rapidly surpass this bascline by round and continue to improve until saturating around round
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. Morcover, 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 self-training in low-data regimes typical of drug discovery. Appendix D. shows an ablation comparing our method with version where designs for each round selected using (trained) predictor the ground-truth oracle.
Conclusion
We introduced generative property enhancer (GPE), 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 simple, scalable, end-to-end, and broadly adaptable solution compatible with diverse generative models and data representations. GPE achieves competitive performance standard offline (non-sequential) protein fitness optimization benchmark and can be iteratively trained on self- self-generated data, successfully applied to an antibody property optimization task.
Our work shares similar limitations to related approaches. First, GPE currently focuses on single- property enhancement, which may not fully meet industry expectations for designs that must simul- taneously adhere to multiple properties of interest. Second, our current validation has thus far been conducted on silico benchmarks. Finally, the iterative sampling process involves some hyperparam- eter 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-rooperty leveraging domain-specific knowledge for targeted applications, and experimenting with multi-modal representations.
property optimization,
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Broader Impact
Design optimization is an important problem in many scientific applications, such as protein engi- neering, 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 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 2D toy task
Here, we analyze the behavior of one of our models-the matched walk-jump sampling-on simple task in 2 dimensions. We start with dataset 186 points whose property value increases as the points move counter clockwise on the spiral. We then create the matched dataset considering a threshold 0.5, = 0.01 and the Euclidean distance between points, with a total of 498 pairs (we use 401 for training). Figure shows the initial and the matched dataset. We proceed by training a m IJJS (we use a simple layers MLP as the denoiser) on the matched dataset and use this model sample new points with (hopefully) increased properties.
15
1.5
1.0
0.0
0.0
-05
0.5
15-
-1.5
-20
-2.
(a) Initial dataset
Matched dataset
Figure 6: (a) Initial dataset, 186 points. (b) Matched dataset, 498 pairs. The data coordinates
between -2 and 2 and the property values range from to 1, increasing counter-clockwise.
Figure 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: 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.
Test sample it:
Thst sample ts:
Test sample id:
Test sample Id:
25
42
sample 4t:4
sumple
Teat sample
Delt sample idh
10.
55
15
50
-28
25
25 25
Figure 7: Examples of generated samples with our model for different initial seeds (marked as cross on the plots). Samples from each iteration are color-coded (blue for first iteration, yellow for the last). The generated samples (i) remain on the manifold of data, (ii) are diverse, and (iii) increase property as we increase the number of iterations.
22

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B Implementation details
B.1 Iterative sampling algorithm
See Algorithm 1.
Algorithm I: lterative Sampling
Data: Model Go seeds 8 = (a, 1 iterations K, n samples per iteration M, distance threshold 6,n n designs N.
Result: Designs {x/]
Do 8;
for k 44-00 0 to 1
// 1. Sample м designs given Dx
Dx+1
(-12x); 2. 2. rejection step
Da+1 f- (aiique(Dx+i)))
Dx+1+ (x)dist(z,ã) (et
end for
Dx e chooossranddomDDr..... N random samples from pool of designs
return D
B.2 Iterative training on self-generated data
See Algorithm 2.
Algorithm 2: Iterative training self- self-generated data
Data: Initial parameters ((0); data distribution p(r); conditional generator qe(x') [x); neighborhood radius A iterations Niter; samples per round M; loss L(::)); initial
matched dataset (0)
Result: Trained parameters ((N
for k 4 to Niter - do
// Generate candidate samples
iid Draw [ ~ p(z); For each i, draw 20~ [x;;;
// 2. Filter enforce neighborhood (and optional property)
(+)) + ((),,)):(((,;,>))) p(()))(
// (Optional) discriminator/orace. filter: keep only (x, D(() with
score ((;;,))
3. Augment training set
M(++1) M+*
// (Optional) deduplicate near-duplicate ictess in (++1)
// 4. Retrain on full set (real pseudo-mat matches)
g(++1) + argmin (0:M())1))
(initialized at (()));
7 end for
return (Naa)
B.3
Matched generative models implementation details
The models on this paper were trained using single A100 Nvidia GPUs and CPU workers per model. Training of different models varies, but they all were trained on less than day. The hyperparameters for training and sampling are the same for all tasks, unless stated differently. They were chosen using subset of the AAV hard task.
23

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m VAE. We use the ResNet architecture proposed in [19]. which has shown to be an efficient encoder- decoder framework for protein design. We extend this to a matched version by implementing a conditional VAF, with the conditioning on being concatenated to = the latent representation. We have one layer of one-hot encoding, followed by 3-layer MI.P resnet blocks with internal layers of size 128. Each m VAE was trained with Adam, learning rate le-1 for AAV and antibodies, and, 1e 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= x L. We chose noise level a= and generate noisy samples by adding gaussian noise to designs, i.e., y = xz + tee E e~ (O.Ia)) We adapt 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 ID 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 T.=2 for AAV dataset, 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 ID U-Net. Here, we adapt the 2D unet proposed by [77] to our ID setting'. We remove the coise-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 total 3.8M parameters, and it is trained with batch size of 256, learning rate le Adam [78] optimizer and a total of 5,000/1, (,00/1,000 ,000 epochs for AAV and GFP, respectively.
Sampling is done following the conditional walk-jump sampling from [60] (see Algorithm in the paper). We use underdamped Langevin MCMC with the discretization scheme proposed by [61] with step size 6 8= and set = 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 seed from the initial set of seeds and uniform + gaussian noise, (1,,8)), where 1/o = U1 (0,1) (0,,a Ia). Each iteration consists of 2 walk steps followed by a jump step, which generates the new sets of design for iteration i. We use the designs generated at iteration to condition the chains on iteration i+ 1, until we reach 20 iterations. Note that we do not re- 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 ID setting. The conditioning mechanism is identical to the original implementation: at each scale we integrate embeddings for the time and seed x (instead 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 Po achieved better performance than the masked distribution (where all tokens masked). We use the implementation from [57] 10, and in particular, their proposed MixtuurreDisseceeeerrrrr ahwp:/eeeeeeeerrrraaaatacaaaaap path with Polynomi al ConvexS chedulleheeeeeeee scheduler (n = 2) and the MixturePatthGneerlliaakk loss. We also use their provided ODE solver with 32 steps (Cond t ieaddiiionalinn
ver). Similar to the m WWS variant, we train for 5,000/1, 1,00 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 and Table 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).
We use the official implementation provided by the authors hithlossinntttss/gtttbb..ocm http:///tttuub...oo////aabb///// We use the codebase provided by the authors: http:///hhhhbooooocccooooeeeeeaa matching.
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Medium difficulty
Hard difficulty
Method
Fitness
Diversity
Novelty
Fitness
Diversity
Novelty
VAE
0.39 (0.01)
(0.3)
(0.6)
0.30(0.02)
14.8 (0.4)
5.00
MAE
0.48 (0.02)
(0.3)
(0.0)
0.38 (0.04)
(1.0
(0.8
FM
0.35 (0.00)
(0.4)
(0.5)
0.27 (0.00)
16.8 (0.2)
(0.()
mFM
(0.00
(.2))
(0.6)
(0.02)
6..3).3)
(0.))
WJS
0.37 (0.01)
14.1 (0.3)
6.8 (0.5)
0.28 (0.00)
(7.3
9.1 (0.3)
mWJS
0.53 (0.01)
(..2)
5.6
0.54 (0.04)
6.6 (0.7)
Table 3: Comparison between (unconditional) models and matched generative models on AAV benchmarks results. Results are shown with mean/standard deviation across 5 runs.
Medium difficulty
Hard difficulty
Method
Fitness
Diversity
Novelty
Fitness
Diversity
Novelty
VAE
0.74 (0.05)
(0.1)
6.3 (0.6)
0.31 (0.02)
6.2 (1.4)
11.6
MVAE
(0.03)
1.9)
(0.7)
0.78 (0.04)
1.3 (0.2)
(0.)
FM
(0.00)
(0.5
9.2 (0.4)
0.08 (0.01)
13.3 (0.4)
11.4
mFM
(0.03)
5.2
(0.0)
0.55 (0.04)
(0.1)
7.7 (0.5)
WJS
-0.02 (0.01)
(2.5)
63.7
-0.06 (0.02)
80.2
61.5
mWIS
(.11
6.0 (0.0)
0.78 (0.02)
2.9 (0.2)
(0.0)
Table 4: Comparison between (unconditional) models and matched generative models GFP bench- marks results. Results are shown with mean/standard deviation across runs.
C.2 Ablation study: influence of the constraint criterion
Table shows ablation studies on the Ag constraint (Levenshtein distance) for the mWJS model on AAV medium task. We observe that fitness remains relatively stable with lower A₂ thresholds (0.50-0.53 for A₂ in 1-7), peaking at 0.53 for A. values of 4, 5, and 6. As A5 increases beyond 7, fitness notably declines, reaching 0.45 at =-1 Diversity generally increases with Az. while novelty shows minor fluctuations. These results indicate that moderate range for Ag (e.g.. 4-7) yields optimal or oparmoptimal fitness. Very small thresholds likely overly restrict generation, while very large thresholds may dilute meaningful local relationships.
2
4
5
6
7
8
9
10
Fitness
.52
.50
.52
.53
.53
.53
.52
.48
.46
.45
Diversity
4.3
6.0
6.0
5.7
5.2
5.3
5.9
6.8
7.3
8.2
Novelty
5.5
5.5
4.6
5.5
5.5
5.5
4.6
5.5
5.0
5.5
Table 5: Ablation study the effect of A, threshold (while keeping A,, fixed at 2)) AAV medium for the mWJS model.
Table 6 shows ablation studies on the A, constraint for the mWJS model on AAV medium task. Here, we observe that performance stable for smaller Ag values. However, fitness declines when Ag exceeds 0.8.
.1
.4
.8
1.0
1.2
g
Fitness
.54
.53
.55
.51
.51
.11
Diversity
5.5
5.2
5.5
5.7
5.3
4.9
Novelty
4.7
5.6
4.7
4.7
4.7
4.7
Table 6: Ablation study on the effect of A, threshold (while keeping A, fixed 5) on AAV medium task.
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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).
Medium difficulty
Hard difficulty
Method
Fitness
Diversity
Novelty
Fitness
Diversity
Novelty
fixed top seeds
0.53 (0.01)
502().2)
(0.))
0.54 (0.04)
4.6 (0.7)
6.5)
random seeds
0.52 (0.02)
5.1 (0.3)
(0.4)
0.53 (0.07)
(0.7)
(.04
Table 7:
Comparison between fixed (5 runs) random initial seeds (100 runs) for AAV medium and hard tasks (mean/std reported).
We observe 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 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 self-generated data
D.1 Ablation study
We performed additional ablation, comparing our original GPE method version where the selected designs for each round are conditioned on a discriminator.
Experimental Setup. We trained ensemble of 15 discriminators, each sharing the m VAE encoder architecture with an added classification head. These discriminators were trained to predict improve- ment labels, T(xr,='). We used the charge pH7 property for consistency with section 4.2. In 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 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-fille filtered version achieved a slight carly-roum improvement. In the table below, RI and are the "Ratio of Improvement" and "Average Improvement".
Method
Round (RI/AD)
Round 2 (RI/AI)
Round 3 (RI/AM AD)
GPE + Discriminator
0.57 0..08
0.67 0.67/0.95 00.92
0.67:00.11700.90 0.80-10.014/1.53 0.78:10.016/1.55
GPE + Oracle
0.63
1.015..11/11.11
GPE (ours)
0.60=0.023/0.98
1.76:..017/1.455
Table 8: Performance comparison of GPE variants across rounds. RI Ratio of Improvement; Al Average Improvement.
We attribute the discriminator's poor performance to domain shift. The discriminator was trained on (xr,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 distr--iistritution for the discriminator. This is reflected in the metrics presented in Table 9,
26

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median
median
median fil::
median fit:
median
median
median
median
median 0.37
median
median
median [i.: 0.24
median fll: 0.27
median fil;; 27
median fil:: 28
median fil.: 0.51
median fit: 0.34
median fit:: 38
median fil:: 0.41
median fil:: 0.44
median fit: 0.47
median fit: 0.48
mediaa BL: 0.23
median fi: 26
median fius
median 0.27
median fit: 0.27
median fiu:
median fiu: 0.26
median fil:: 0.26
median 0.26
median fit: 0.26
median
1.40
8.30
median
median fit. 0.55
FR.: 0.24
fi:: 0.35
fit:: 4.43
1it. 0.49
fit. 0.51
fit: 0.52
fit: 0.52
fit.: 0.53
fit.: 0.54
fit. 0.55
median fit: 0.56
fR.: 0.27
fl::: 0.33
fit:: 37
fit. 0.37
flt. 0.41
fit.: 0.45
flt: 0.47
fit. 0.51
fit.: 0.53
fit. 0.54
Initial
Iteration
Iteration
Iteration
Iteratioo
Iteration
Figure 8: Protein fitness improvement as number of iterations increase. We start from single random seed and use the mWJS model trained on AAV hard to sample designs. The plots show the distribution of fitness of designs for a different initial seeds not seen during training (rows) at different sampling iterations (columns). The first column show the fitness the initial seed.
Evaluation Set
Accuracy
Precision
Recall
Variance
On 10% Holdout Set (IID) On GPE Designs
0.94=0.005 0.609
1.00
0.93
0.007
0.002
0.029
0.021
Table 9: Discriminator performance on IID and out-of-disttributio (GPE) data.
D.2
Diversity analysis
Not all seeds are equal. For some which have more neighbors, i.e. 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, each round the number of designs (diversity) per seed goes down both in terms of mean and standard deviation.
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Statistic
Round
Round 2
Round
Count
3,554
4,054
4,319
Mean
3.43
2.06
1.71
Std
14.28
7.63
5.86
Min
1.00
1.00
1.00
Max
101.00
101.00
101.00
Table 10: Descriptive statisties of GPE-generater designs across rounds.
E
Wet-lab validation
As additional empirical evidence we provide 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 33.44% vs. 4.8%). Additional experiments benchmarking VAE vs mPProEn are in progress and will be added to the manuscript 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, artificially create 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 the digit rotated with highest angle, i.c., given two random angles 0 and 0g s.t. 01 02 < 30 and 01 > 22. then g( (R(x,01)) g( ((((r,2)).
We train 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).
9
9
9
9
9
9
9
9
9
9
9
9
9
9
2
2
2
2
2
2 2
2
2 2
2
2
2
2
2
2
2
Figure 9: Qualitative results rotating MNIST. Given unseen digit (the first the sequence), model sample digits that have higher property (i.e. are more clockwise rotated). Each figure is single MCMC chain generated by the masked walk-sampling model.
28


Reviews:
[{"review_id": "kxd9vandsA", "reviewer": "Reviewer_fsEJ", "summary": "This 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.", "questions": "1) 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.", "limitations": "NA", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength: 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", "was_revised": true, "final_justification": "Satisfied with the author's responses, conditioned on the promised modifications to be made to the final paper.", "rebuttal": "We thank the reviewer for their reviews and for highlighting the key strength of our work: the ability to perform design optimization without relying on unreliable surrogate estimates, particularly crucial in low-data and underexplored regions of the design space. Below we address the reviewer's concerns.\n\n**Lack of theoretical novelty.** We respectfully disagree with the assessment that our theoretical contribution lacks novelty. While Theorem 1 adapts a known maximum likelihood result, its application within our framework is novel (and foundational) for GPE. In particular, we demonstrate that by formulating design optimization as a conditional density estimation problem and leveraging the **implicitly defined \"improved distribution\" $p^+(x'∣x)$ through data matching, we can theoretically recover the optimal conditional density without any explicit property predictor**. This theoretical grounding provides the basis for training diverse off-the-shelf generative models to directly sample improved designs, which is a significant departure from conventional predictor-guided optimization paradigms. The novelty lies in how this theoretical result enables a simple, end-to-end, and predictor-free approach to a challenging problem.\n\n**\"Match variants are simply conditional generative models\".** The underlying generative models (VAE, flow matching, walk-jump sampling, diffusion, autoregressive, etc.) are indeed  \"off-the-shelf\" in their core formulation. However, the novelty is not in inventing new generative model architectures, but in the GPE framework itself and how it trains and applies these existing models to tackle the design optimization problem. The key innovations are:\n\n* **The \"matched dataset\" construction:** This novel data pairing ($ (x,x’)$  where $x'$ has higher property than $x$) implicitly encodes the desired property improvement.\n\n* **The conditional density estimation problem formulation:** We cast the problem as learning to sample from $p^+(x'∣x)$, the distribution of improved designs conditioned on a seed, which is implicitly defined by the matched data.\n\n* **Predictor-free optimization:** By training these conditional generative models directly on the matched dataset using objectives aligned with conditional density estimation (e.g., maximum likelihood or its approximations), GPE bypasses the need for a separate, often unreliable, discriminative property predictor. Therefore, while the generative models themselves are known, their instantiation within the GPE framework for implicit, predictor-free design optimization represent the core novelty.\n\n**\"Fix the reference to 'the least squares loss 3.2' in line 172. What is it referring to?\"** The reference \"least-squares loss (3.2)\" should refer to the mWJS loss defined on L166 ($\\mathcal{L}_{mWJS}$), which is a least-squares loss. We will assign a specific equation number to the mWJS loss and refer to it in the revised manuscript.\n\n**\"In each training round, how many samples are generated per conditioning seed sequences? Have you performed any ablation on the number of samples generated per seed? Does it have a significant impact?\"** This is an interesting question and we thank the reviewer for raising it. Indeed, 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.\n\nUnfortunately, we cannot include figures in the rebuttal but we will add more intuition and ablation plot on this point in the updated version of the manuscript. For the moment, we hope the following statistics from an ablation will answer your question.\nWe 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.\n\n| **Statistic** | **round 1**  |  **round 2**  | **round 3**  |\n|-----------|------------|------------|------------|\n| count     | 3554       | 4054       | 4319       |\n| mean      | 3.43   | 2.06   | 1.71   |\n| std       | 14.28  | 7.63   | 5.86   |\n| min       | 1.00   | 1.00| 1.00   |\n| max       | 101.00 | 101.00 | 101.00 |\n**Table 1:** Statistics on number of designs per seed over multiple rounds.\n\n**M_k mismatch between Section 3.4 and Algorithm 2.** We apologize for this inconsistency in notation—thank you for pointing out. The correct version is the one described in Section 3.4 (L197). We will fix Algorithm 2 in the revised manuscript, ensuring consistency between the main text and the appendix. Please find below the essential changes that correct the error:\n```\nP^(k) ← { (x_i, x'_i) : dist( x'_i, x_i ) ≤ Δ_x }\nM^(k+1) ← M^(k) ∪ P^(k)  // Augment training set\n// 4. Retrain on the full (real + pseudo) matches\nθ^(k+1) ← argmin_{θ}  L( θ; M^(k+1) )\n```\n\n**Fixed initial seeds vs random initial seed during benchmarking.** For benchmarking, we used fixed initial seeds after observing no considerable performance difference with random seeds in preliminary tests. This allowed us to isolate and systematically compare optimization algorithms from a standardized starting point. \n\n| Seed Type | fitness | diversity | novelty |\n|-----------|---------|-----------|---------|\n| fixed seed | .53 (.01) | 5.2 (.2) | 5.6 (.6) |\n| random seed | .54  (.02) | 5.3 (.3) | 5.4 (.5) |\n**Table 2:** fixed vs random seed on AAV-med (mean/std over 5 rounds)\n\nFor the AAV-medium dataset (Table 2), the performance across all metrics (fitness, diversity, and novelty) remains highly 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.\n\n\n| Seed Type | fitness | diversity | novelty |\n|-----------|---------|-----------|---------|\n| fixed seed | .54 (.04) | 4.6 (.7) | 6.6 (.5) |\n| random seed | .52 (.06) | 4.1 (.8) | 6.8 (.4) |\n**Table 3:** fixed vs random seed on AAV-hard (mean/std over 5 rounds)\n\nSimilarly, for the more challenging AAV-hard dataset (Table 3), the mWJS model demonstrates robust performance. While minor fluctuations are present, the fitness, diversity, and novelty scores for both fixed and random seeds remain comparable, reinforcing our preliminary findings that the choice of initial seed does not considerably impact the algorithm's performance.\n\nThis corroborates our initial observations and confirms that the use of fixed seeds provides a reliable basis for comparison without sacrificing the generalizability of our findings. We will include this ablation experiment in the final version of the manuscript.\n\n**Missed citation:** The citation of Ghaffari et al. (2024) will be explicitly added to the related work section. Thanks for pointing it out."}, {"review_id": "IO4oHC55mx", "reviewer": "Reviewer_VQoe", "summary": "This 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.", "questions": "Please see Strengths And Weaknesses section.", "limitations": "It 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.", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 1, "clarity": 2, "significance": 1, "originality": 2, "strengths_and_weaknesses": "- 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.", "was_revised": true, "final_justification": "I appreciate and thank the authors for their reply to my questions. Unfortunately, my main concerns still remain outstanding. There were multiple new things that were introduced in the rebuttal period to motivate the paper which were not described in the original paper. For example, the description that the paper tackles offline optimization problem was made clear only in the rebuttal. The original paper situates itself within a very different class of problems. The authors provided a survey on offline optimization during rebuttal which shows there is a lot of work on the offline optimization problem but none of i was discussed in the original paper. I also believe the baselines are weak. Therefore, I keep the same original review score. \n\n**Having said that, I am going to go with the consensus of the rest of the reviewers and would be okay if the paper is accepted.**", "rebuttal": "We thank the reviewer for their feedback on Bayesian optimization (BO) and discriminative models. We believe there may be a misunderstanding of GPE's **offline (one-round) optimization** problem setting (see [Kim et al 25] for a survey on this topic), which fundamentally differs from iterative online/Bayesian optimization. Reviewer _DwTD_  acknowledges this difference. We hope the following paragraphs can make this distinction clearer. We will incorporate these clarifications in the paper and better contextualize the problem setup.\n\n[Kim et al, 25] Offline Model-Based Optimization: Comprehensive Review.\n\n**Problem formulation and \"strawman\" argument.** We thank the reviewer for a thoughtful critique and for pointing us to [Tripp & Hernández‑Lobato 2024]. This work relies on the PMO benchmark (from [Gao et al 22]), a simplified setting consisting of surrogate properties of relatively simple properties on small molecules only. As the authors state in the discussion themselves,\"what this paper presents should best be thought of as a very limited pilot study\" and \"it is unclear whether results from single-task, noiseless, and unconstrained optimization will translate to real-world problems which tend to be multitask, noisy, and highly constrained.\"\n\nBelow we clarify the scope of our claim, provide empirical evidence that reliable discriminative surrogate models remain an unsolved bottleneck for many real‑world molecular and protein design tasks, and explain why BO, while indispensable, is not always a universal remedy in these settings.\n\n* **We agree BO is valuable when the surrogate is trustworthy.** [Tripp & Hernández‑Lobato 2024] show that careful priors, and optimizer settings let BO top the PMO small‑molecule benchmark. \n\n* **But, for most real objectives the surrogate remains the weak link, eg**:\n    - _Protein stability (ΔΔG)_: state‑of‑the‑art models still hover around RMSE ≈ 1–2 kcal/mol and r ≈ 0.5 on fully independent test sets—above the ≤0.5 kcal/mol engineering threshold [Benevuta et al 23].\n    - _Protein‑ligand affinity_: removing train–test leakage in PDBBind drops Pearson r to ≤ 0.30. [Li et al 24]\n    - _Small‑molecule phys‑chem (e.g. log S)_: OOD splits double the error reported on random splits. [Sorkun et al 19]\n\n* **When surrogates are unreliable, BO inherits three practical failure modes.**\n    - _Long‑tail bias_: the acquisition function is steered away from the true optimum by systematic surrogate error at the distribution edges (documented in the affinity study above).\n    - _High‑dimensional/discrete spaces_: recent survey finds no GP‑ or neural‑BO variant that scales gracefully beyond ~100 categorical dimensions. [González-Duque et al 24]\n    - _Fragility and mis‑calibration_: tiny changes in prior width or kernel smoothness erase BO’s edge, and uncertainty estimates in GNNs and protein‑fitness models remain poorly calibrated. [Greenman et al 25]\n\n* **Our contribution targets precisely this early regime.** We learn local generative distributions that do not need a global oracle. Once higher‑quality experimental labels accumulate, the BO frameworks championed by the reviewer can be layered on top of our generator as a natural next step.\n\nWe will revise the introduction and discussion to reflect this balanced view: **_BO excels with reliable surrogates; our method tackles the many cases where such surrogates are not yet available_**.\n\n[Benevenuta et al 23] Challenges in predicting stabilizing variations: An exploration\n\n[Li et al 24] Leak Proof PDBBind: A Reorganized Dataset of Protein-Ligand Complexes for More Generalizable Binding Affinity Prediction\n\n[Sorkun et al 19] AqSolDB, a curated reference set of aqueous solubility and 2D descriptors for a diverse set of compounds\n\n[González-Duque et al 24] A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences\n\n[Greenman et al 25] Benchmarking uncertainty quantification for protein engineering\n\n**GGS and \"smoothed fitness landscape\".** We agree that GGS's \"smoothed fitness landscape\" aims to mitigate real-world challenges related to noisy/rugged fitness landscapes. Our \"predictor-free\" approach is not presented as the only necessary paradigm shift, but rather as a potential alternative that sidesteps the complexities and potential pitfalls (eg,  overfitting or unreliability at tails) associated with training and relying on an explicit discriminative predictor for design generation in an offline context. GPE provides a conceptual simplicity and potential robustness by implicitly learning property improvement, instead of explicitly modeling or smoothing the fitness landscape. \n\nOur method is orthogonal to GGS (or any other model that leverages a predictor) and could be combined for enhanced offline optimization. As mentioned above, these methods could also be integrated into BO loops. We will clarify this in the related work section.\n\n**Modern Bayesian optimization approaches with deep generative models.** Recent BO models integrate deeply with generative models, using them to navigate complex, structured design spaces. However, we reiterate that these approaches are still embedded within the online, iterative framework of BO, where the generative model often aids in proposing candidates for subsequent evaluation guided by an acquisition function derived from a surrogate model.  On the other hand, GPE was made for one-shot batch generation for offline applications. We will integrate these references into related works to provide a more comprehensive overview of how generative models are used in both online and offline optimization contexts. \n\n**Ablation study of C(x,x’).** We conducted ablation studies on the $\\Delta_x$ (Levenshtein distance) and $\\Delta_g$ (property improvement) thresholds, as shown in the tables below for mWJS on the AAV-medium and AAV-hard datasets.\n\n_Ablation study of $\\Delta_x$ thresholds:_\n\n| $\\Delta_x$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |\n|--------|---|---|---|---|---|---|---|---|---|---|\n| **fitness** | .52 | .50 | .52 | .53 | .53 | .53 | .52 | .48 | .46 | .45 |\n| **diversity** | 4.3 | 6.0 | 6.0 | 5.7 | 5.2 | 5.3 | 5.9 | 6.8 | 7.3 | 8.2 |\n| **novelty** | 5.5 | 5.5 | 4.6 | 5.5 | 5.5 | 5.5 | 4.6 | 5.5 | 5.0 | 5.5 |\n**Table 1**: AAV-med dataset for varying $\\Delta_x$.\n\nFor the AAV-medium (Table 1), we observe that fitness remains relatively stable with lower $\\Delta_x$ thresholds (0.50-0.53 for $\\Delta_x$ in 1-7), peaking at 0.53 for $\\Delta_x$ values of 4, 5, and 6. As $\\Delta_x$ increases beyond 7, fitness notably declines, reaching 0.45 at $\\Delta_x$=10. Diversity generally increases with $\\Delta_x$, while novelty shows minor fluctuations.\n\n| $\\Delta_x$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |\n|--------|---|---|---|---|---|---|---|---|---|---|\n| **fitness** | .26 | .35 | .37 | .32 | .54 | .54 | .52 | .46 | .35 | .31 |\n| **diversity** | 18.2 | 10.5 | 4.7 | 5.9 | 4.6 | 4.5 | 3.8 | 4.8 | 7.6 | 10.1|\n| **novelty** | 0 | 3 | 3 | 5 | 6.6 | 7 | 7 | 6 | 8 | 5|\n**Table 2**:  AAV-hard dataset for varying $\\Delta_x$.\n\nOn AAV-hard (Table 2), fitness displays a more pronounced sensitivity to $\\Delta_x$. It starts lower, increases, and reaches its peak at 0.54 for $\\Delta_x$ values of 5 and 6. Performance significantly underperforms for very small $\\Delta_x$ (0.26 at $\\Delta_x$=1) and also deteriorates for large $\\Delta_x$ (>7), dropping to 0.31 at $\\Delta_x$=10.\n\nThese results indicate that a moderate range for $\\Delta_x$ (e.g., 4-7 for AAV-medium, 5-6 for AAV-hard) yields optimal or near-optimal fitness. Very small thresholds likely overly restrict generation, while very large thresholds may dilute meaningful local relationships.\n\n_Ablation study of $\\Delta_g$ thresholds ($\\Delta_x$ fixed at 5):_\n\n| $\\Delta_g$ | .1 | .2 | .4 | .8 | 1 | 1.2 |\n|--------|-----|-----|-----|-----|---|-----|\n| **fitness** | .54 | .53 | .55 | .51 | .51 | .51 |\n| **diversity** | 5.5 | 5.2 | 5.5 | 5.7 | 5.3 | 4.9 |\n| **novelty** | 4.7 | 5.6 | 4.7 | 4.7 | 4.7 | 4.7 |\n**Table 3**: AAV-med dataset for varying $\\Delta_g$.\n\n| $\\Delta_g$ | .1 | .2 | .4 | .8 | 1 | 1.2 |\n|--------|-----|-----|-----|-----|---|-----|\n| **fitness** | .52 | .54 | .53 | .46 | .45 | .36 |\n| **diversity** | 4.8 | 4.6 | 6.3 | 6.0 | 7.2 | 1.6 |\n| **novelty** | 6.6 | 6.6 | 6.6 | 5.7 | 5.7 | 2.8 |\n**Table 4**: AAV-hard dataset for varying $\\Delta_g$.\n\nTables 3 and 4 report an ablation study where we vary the $\\Delta_g$ threshold (while keeping $\\Delta_x$ fixed at 5). Here, we observe that performance is stable for smaller $\\Delta_g$ values. However, fitness starts to decline notably when $\\Delta_g$ exceeds 0.8, particularly evident in the AAV-hard dataset.\n\nWe will include a detailed discussion of this comprehensive ablation study in the revised manuscript.\n\n**“Why is GPE’s approach better than the principled exploration/exploitation tradeoff we get from model uncertainty based optimization of Bayesian optimization?”** GPE is not _better_ than Bayesian Optimization (BO), but it's a different approach. While both BO and GPE aim at design optimization in small sample sizes, the two frameworks solve different problems. The goal of GPE is to generate designs, whereas in BO the goal is to choose the most promising designs that should be labeled in order to improve predictors’ performance or find the best candidate—i.e. the focus is selection. In the context of optimizing designs with deep generative models, one would have a suite of (1) generative models, (2) property predictors and (3) BO/active learning modules that will do the final selection across a pool of candidates. GPE falls in (1), the category of generative models section that will contribute to the library of potential candidates. Thus, GPE complements BO; it's ideal for producing promising design batches for costly offline validation, or can be integrated into BO for warm-starting or batch acquisition."}, {"review_id": "J2rzznk0D4", "reviewer": "Reviewer_DwTD", "summary": "This 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.", "questions": "Questions:\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.", "limitations": "The limitations are adequately addressed, once the focus on offline optimization etc. is clarified.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\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.", "was_revised": true, "final_justification": "This is a promising method -- and the reviewers dealt with my major concerns. Raising my score accordingly. The reviewers will need some confidence intervals on their discriminator results however.", "rebuttal": "We thank the reviewer for the comprehensive and insightful review. We appreciate the positive comments on the simplicity, intuition, empirical effectiveness, modularity of our framework and that our work is \"fascinating, and a very promising direction\". We also thank the extra references, which will be added to the manuscript. Next, we address each of the reviewer's points and suggestions.\n\n**Clarifying problem setting.** We will clarify in the introduction and problem setting that our work focuses on offline (one-round) design optimization, ie generating improved designs from seeds without iterative experimental feedback. As pointed by the reviewer, our iterative sampling and self-training are distinct from online/Bayesian optimization. This was indeed a source of confusion to Reviewer _VQoe_. We will also explicitly state that we directly learn new conditional generative models, rather than guiding pre-trained models. We briefly discussed this on Appendix A, but we will make it clearer on the main manuscript.\n\n**How important is using C(x,x') to prevent “out-of-domain” generation?** The constraint $C(x,x')$ is important for preventing \"out-of-domain\" generation in GPE. This term, particularly the distance component like $\\text{dist}(x,x')<\\Delta x$​, ensures that the generated design $x'$ remain within a meaningful vicinity of its seed $x$. Without such constraint, the generative model could produce samples that are technically \"improved\" in property but are entirely unrealistic, or irrelevant to the original design domain. By construction, training on matched datasets provides theoretical guarantees for generating designs in distribution (as dx goes to 0), please see Theorem 2 in [Tagasovska et al 2024].\n\nThis is also relevant to the self-training strategy, as one of the primary concerns in such setups is model collapse—specifically, overfitting on synthetic data and forgetting the original training distribution. Current methods to mitigate model collapse typically involve either controlling the ratio of original to synthetic data or pruning synthetic examples that deviate significantly from the training data. Training on matched datasets, by design, inherently addresses both of these concerns. \n\n**Ablation on** $\\Delta_x$: Below we show the performance of mWJS trained on different matched data from both AAV-medium and AAV-hard, with varying $\\Delta_x$ threshold.\n\n| $\\Delta_x$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |\n|--------|---|---|---|---|---|---|---|---|---|---|\n| **fitness** | .52 | .50 | .52 | .53 | .53 | .53 | .52 | .48 | .46 | .45 |\n| **diversity** | 4.3 | 6.0 | 6.0 | 5.7 | 5.2 | 5.3 | 5.9 | 6.8 | 7.3 | 8.2 |\n| **novelty** | 5.5 | 5.5 | 4.6 | 5.5 | 5.5 | 5.5 | 4.6 | 5.5 | 5.0 | 5.5 |\n**Table:** Results of mWJS on AAV-med dataset for varying $\\Delta x$.\n\nFor the AAV-medium dataset, we observe that fitness is relatively stable with lower thresholds (0.50-0.53 for $\\Delta_x$ in 1-7), peaking at 0.53 for $\\Delta_x$ values of 4, 5, and 6. As $\\Delta_x$ increases beyond 7, fitness notably declines, reaching 0.45 at $\\Delta_x$=10. \n\n| $\\Delta_x$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |\n|--------|---|---|---|---|---|---|---|---|---|---|\n| **fitness** | .26 | .35 | .37 | .32 | .54 | .54 | .52 | .46 | .35 | .31 |\n| **diversity** | 18.2 | 10.5 | 4.7 | 5.9 | 4.6 | 4.5 | 3.8 | 4.8 | 7.6 | 10.1|\n| **novelty** | 0 | 3 | 3 | 5 | 6.6 | 7 | 7 | 6 | 8 | 5|\n**Table:** Results of mWJS on AAV-hard dataset for varying $\\Delta x$.\n\nOn the AAV-hard dataset, fitness displays a more pronounced sensitivity to $\\Delta_x$. It starts lower, increases, and reaches its peak at 0.54 for Δx​ values of 5 and 6. Performance significantly underperforms for very small $\\Delta_x$ (0.26 at $\\Delta_x$=1​) and also deteriorates for large $\\Delta_x$ (>7), dropping to 0.31 at $\\Delta_x$=10.\n\n**Do you think the empirical performance of this method is from the increased training set size and (discriminator free) implicit improvement objective?** We believe GPE's performance stems from both the increased effective training data (via matched pairs) and the discriminator-free implicit objective. While a hypothetical discriminator-based model could use similar paired data, GPE's key advantage is its simplicity and avoidance of a separate predictor training loop. GPE, which is formulated as a conditional density estimation problem, implicitly learns the distribution of improved samples rather than relying on a (potentially unreliable) point-wise prediction.\n\nMoreover, introducing an auxiliary discriminative model adds non-trivial complexity to the overall pipeline (training two models, positive/negative sample reweighting, managing their interaction, potential for mode collapse or training instabilities if not carefully balanced). GPE's end-to-end, single-stage training bypasses these issues somehow.\n\n**Do you think there would be less need for iterative self training using a trained predictor on matched data?** The iterative self-training helps for extrapolation, a benefit for which a reliable explicit discriminator might also reduce the need. But, obtaining such a discriminator (specially in low-data) is often the bottleneck itself. That being said, we note that our method is orthogonal to predictor-based methods, and therefore could use any discriminator to further guide generation, potentially combining the benefit of both approaches.\n\n**Limitations of ML Oracles.** We agree with the reviewer's point regarding ML oracle limitations and acknowledge this in the manuscript (footnote 6, page 7). We use them for fair comparison with well-established benchmarks [Kirjner et al.]. We would also like to also emphasize the antibody experiment (Section 4.2) as an example of GPE extrapolating on a physicochemical property with an exact evaluation metric, serving as a form of \"oracle-free\" validation. \n\n**How does this work relate to DPO/preference learning.** GPE shares the spirit of preference learning, aligning models with desired outcomes based on comparisons. Similar to DPO, we optimize directly without an explicit reward model or property oracle. Both frameworks theoretically show their paired objectives implicitly optimize the same quantity as explicit reward-maximizing procedures: DPO with a binary-cross-entropy loss on preference pairs, and GPE by learning a conditional density estimator on matched data. This \"bakes\" the optimization signal into the generator, yielding simpler, more stable training loops.\nConceptually there are similarities between the two frameworks, but, we would like to highlight the following differences where using the matched reconstruction is beneficial:\n\n* Automatic data densification: Matching inflates an n-point dataset to O(n2) ordered pairs, providing richer, automatically generated supervision than human-annotated sets.\n* On-manifold generation: Nearest-neighbor matching ensures plausible, realistic generations within the data manifold, unlike DPO which can drift with thin preference coverage.\n* Domain agnosticism & small-data robustness: GPE requires no language-specific likelihoods or large pre-trained policies, making it practical for scientific design where DPO's ratios are unavailable or poorly calibrated.\n\nIn short, both bypass discriminators/reward models,, but GPE's matched-pair strategy converts readily-available scalar property data into a dense, on-manifold, gradient-approximating signal---often cheaper and more informative than explicit preference labels.\n\n**Notation $y$ in the Lagrangian.** The functional derivative acts by $\\frac{\\delta}{\\delta q(x'|x)} q(y'|y) = \\delta(x-y) \\delta(x'-y')$ where the rhs denotes Dirac delta distributions. Marginalization over the dirac delta distributions then changes the arguments of the densities from $y$, $y'$ to $x$, $x'$ as required for the result stated in the theorem. All four variables $x$,$x'$, $y$, $y'$  take value in the same space. We will make this explicit in the proof and clarify the role of $y$.\n\n**R^d (continuous) vs. V^D (discrete)**. We will clarify that the Rd formulation is for generality, and its application to discrete sequences is direct via appropriate architectural choices.\n\n**Intractability of Z(x).** We will add a clarifying sentence that Z(x) (the normalization constant in Equation 1) is generally intractable due to high-dimensional integration/combinatorial summation, which justify our likelihood approximation approach.\n\n**“Tangential question”: GPE’s implicit exploration/exploitation tradeoff.**  We 100% agree with the reviewer that “for offline optimisation tasks, we are more interested in exploitation (modulo diverse batch-design concerns)”. Therefore, GPE's primary mechanism is exploitation: it learns to generate designs ($x'$) that have higher property values ($g(x')>g(x)$) than given seeds ($x$), based on observed improvements in the training data. This is a strong drive towards known high-value regions. The iterative sampling further refines this exploitation. \n\nHowever, GPE also exhibits some level of implicit exploration: it generates a distribution of improved designs, allowing exploration within high-value regions. The distance constraint ($\\text{dist}(x,x')<\\Delta_x$​) encourages localized exploration, ensuring generated designs remain near their seeds. Following [Kirjner et al. 24]'s suggestion, the Fitness metric can be interpreted as a proxy for exploitation, while the Novelty and Diversity can provide insights about exploration/exploitation trade-offs. Finally, iterative self-training can potentially enable GPE to extrapolate property values and explore regions beyond the original training data manifold by generating synthetic data and retraining, representing a more global, model-driven form of exploration. \n\nGPE does not use explicit acquisition functions but inherently balances strong exploitation with localized, and eventually broader, exploration through its generative mechanism, constraints, and self-training."}, {"review_id": "tgWz59ScT3", "reviewer": "Reviewer_uogt", "summary": "This 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.", "questions": "1.\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?", "limitations": "yes", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\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.", "was_revised": true, "final_justification": "The authors’ responses have addressed most of my initial concerns.  I finally decided to borderline accept this paper.", "rebuttal": "We thank the reviewer for their positive assessment, particularly acknowledging GPE's simplicity, data efficiency, and architecture-agnostic nature.\n\n**Limited real-world validation.** _In silico_ initial validation is standard for novel computational design methods, given the significant cost and time of _in vitro_ studies. As additional empirical evidence we provide a summary of single-round wet-lab experiments comparing GPE (mPropEn variant) against LAMBO [Gruver et al 23] for improving therapeutic protein binding affinity across eight initial seeds over three distinct targets. Due to proprietary constraints, we do not disclose the targets. Our model demonstrates significantly higher and more consistent binding rates (94.6% vs. 44.2% overall) and design improvements (34.4% vs. 14.0% overall). \n\n[Gruver et al 23] Protein design with guided discrete diffusion.\n\n**Multi-objective design challenges and experiments.** This reviewer raised a valid concern, as simultaneously improving multiple criteria can result in sparse matched pairs. To address this, we compute a multivariate rank across all properties of interest and optimize for that single scalar score. This multivariate score can be derived using either the Hypervolume [Zitzler et al 03] or the CDF indicator, as proposed in [Park et al 24]. Both methods effectively mitigate the sparsity issue by reducing the problem to a single optimization target.\n\nWe demonstrate this approach on a multi-property antibody optimization task, selecting two orthogonal developability properties: positive charge and negative charge. We compute a multivariate ranking over these two properties to obtain a single scalar score used for matching. We then train individual single-property GPE (mPropEn variant, as described in the manuscript) models to optimize each property separately, as well as a multi-property GPE (multiGPE) model that directly optimizes the combined multivariate ranking score.\n\n| Model / Score         | HV     |\n| :-------------------- | -----: |\n| multiGPE              |   0.39 |\n| GPE neg charge        |   0.12 |\n| GPE pos charge        |   0.22 |\n**Table:** Fraction of designs from each PropEn model that are in the top 20% of Pareto-optimal candidates when scored by hypervolume (HV).\n\nWe observe that multiGPE consistently suggests more designs that lie on the Pareto front, whereas the single-objective models tend to generate designs that occupy the extremes (tails) of the front. Furthermore, when considering both objectives, the most optimal designs on the Pareto front are predominantly proposed by multiGPE variants. This supports the effectiveness of combining our matching strategy with multi-objective indicators. Further datasets and experiments will be explored in subsequent analyses.\n\n[Zitzler et al 03] Performance assessment of multiobjective optimizers: An analysis and review\n\n[Park et al 24] BOtied: Multi-objective Bayesian optimization with tied multivariate ranks\n\n**Applying GPE within a diffusion framework.** Diffusion models and flow matching models (when source distribution is Gaussian—as in our case) are equivalent under some reparametrization (eg, see the nice explanation in [Gao et al 25]). Therefore, we anticipate that results with “matched diffusion models” would be similar to those of our mFM (matched flow matching). Moreover, mWJS (matched walk-jump sampling) instantiation is a score-based model, closely related to diffusion models. Implementing GPE with a full diffusion framework would involve defining a conditional diffusion process and learning its conditional score function, similar to how $p^+(x'|x)$ is defined.\n\n[Gao et al 25] Diffusion Meets Flow Matching: Two Sides of the Same Coin\n\n**Sensitivity to number of iterations.** Our empirical results in Figures 3 (a and b) demonstrate that GPE's performance, in terms of median fitness, rapidly increases and then plateaus after a certain number of iterations (e.g., around 10-12 for AAV on protein fitness, and 4 rounds for GFP). This suggests a (dataset-dependent) saturation point where further iterations yield diminishing returns, providing practical guidance for iteration choice. We noted that the models’ \"hyperparameters are transferable between the protein tasks studied, suggesting some degree of robustness\" (L324)."}]

Author rebuttal:

Meta-review: This paper introduces the *Generative Property Enhancer (GPE)*, a conditional density estimation approach that aims to improve molecular and protein design without relying on surrogate discriminators. The idea of leveraging ordered property pairs to implicitly guide the generative model is appealing, and the authors present results on protein fitness optimization benchmarks. Reviewers appreciated the motivation to move beyond surrogate models, the simplicity and scalability of the approach, and the additional ablations and experiments provided during rebuttal. 

Several reviewers highlighted that their earlier concerns were adequately addressed: reproducibility was improved through ablations, and the baselines were expanded. On the other hand, some of reviews indicated limited novelty since the generative models themselves are not fundamentally modified, as well as  concerns about problem specification and positioning, in particular the relation to offline optimization. Based on this, the AC strongly requires that for the camera-ready version, the authors incorporate the clarifications and improvements promised in the rebuttal, including a more thorough integration of the offline optimization literature, and stronger comparisons. This also concerns  the wet-lab validation, which was very shortly mentioned in the rebuttal. The wet-lab validation should be described thoroughly, specifying the experimental conditions, evaluation metrics, the way the candidates were selected for experimental validation, the targets, and how exactly the experimental success rate was compared against LAMBO, etc. Without providing these details, these important results are not reproducible. With these recommended refinements, the paper will make a solid and impactful contribution to the NeurIPS community.
Decision: Accept (poster)