Exploring Chemical Space with Score-based Out-of-distribution Generation
Authors: Seul Lee
Jaehyeong Jo
Sung Ju Hwang
Venue: Submitted to ICLR 2023 (2023)
Keywords: molecule generation
score-based generative modeling

Abstract: A well-known limitation of existing works on molecule generation is that the generated molecules highly resemble those in the training set. To generate truly novel molecules with completely different structures that may have even better properties than known molecules for de novo drug discovery, more powerful exploration in the chemical space is necessary. To this end, we propose Molecular Out-Of-distribution Diffusion (MOOD), a novel score-based diffusion scheme that incorporates out-of-distribution (OOD) control in the generative stochastic differential equation (SDE) with simple control of a hyperparameter, thus requires no additional computational costs unlike existing methods (e.g., RL-based methods). However, some novel molecules may be chemically implausible, or may not meet the basic requirements of real-world drugs. Thus, MOOD performs conditional generation by utilizing the gradients from a property prediction network that guides the reverse-time diffusion process to high-scoring regions according to multiple target properties such as protein-ligand interactions, drug-likeness, and synthesizability. This allows MOOD to search for novel and meaningful molecules rather than generating unseen yet trivial ones. We experimentally validate that MOOD is able to explore the chemical space beyond the training distribution, generating molecules that outscore ones found with existing methods, and even the top 0.01% of the original training pool.

Under review as a conference paper at ICLR 2023
EXPLORING CHEMICAL SPACE WITH SCORE-BASED OUT-OF-DISTRIBUTION GENERATION
Anonymous authors Paper under double-bling review
ABSTRACT
A well-known limitation of existing molecular generative models is that the gener- ated molecules highly resemble those in the training set. To generate truly novel molecules with completely different structures that may have even better properties than known molecules for de novo drug discovery, more powerful exploration in the chemical space is necessary. To this end, we propose Molecular Out-Of-distribution Diffusion (MOOD), novel score-based diffusion scheme that incorporates out-of- distribution (OOD) control in the generative stochastic differential equation (SDE) with simple control of hyperparameter, thus requires no additional computational costs unlike existing methods (e.g., RL-baaed methods). However, some novel molecules may be chemically implausible, or may not meet the basic requirements of real-world drugs. Thus, MOOD performs conditional generation by utilizing the gradients from a property prediction network that guides the reverse-time diffusion process to high-scoring regions according to multiple target properties such protein-ligand interactions, drug-likenn Likgglikeness, and synthesizability. This allows MOOD search for novel and meaningful molecules rather than generating unseen yet trivial ones. We experimentally validate that MOOD is able to explore the chemical space beyond the training distribution, generating molecules that outscore ones found with existing methods, and even the top 0.01 % of the original training pool.
INTRODUCTION
Finding novel molecules with desired chemical properties is the primary goal of drug discovery. However, the chemical space is vast, and it is infeasible to examine all possible molecules to find those satisfying a target molecule profile. Recently, deep molecule generation models that can automatically generate candidate molecules arose promising substitutes (Gómez-Bombarrlli et al., 2016; Lim et al., 2018; Schwalbe- Koda & Gómez Boaneeze-Bbbbrllii,,, 2019) for conventional experimental drug discovery approaches via trial-and-error processes with human efforts. However, most existing molecule generation models have the following two limitations, which limit their practical impact.
First of all, the common pitfall of the models based distributional learning is that the exploration confined to the training distribution, and the generated molecules highly resemble those in the training set. For example, Walters & Murcko (2020) point out that the top-scoring molecule found by the model of Zhavoronkov et al. (2019) exhibits "striking similarity" to known active molecules included in the training set (see Figure (Left; al, a2)). This highly limits its applicability de novo drug discovery which aims to find completely new molecules rather than slight variations of existing ones, emphasizing the need for a generation strategy that can generate distrribbtii (OOD) molecules with desired properties.
Secondly, there exists a discrepancy between the target chemical properties of the molecule generation models and those in real-world scenarios. The most common properties utilized by the molecule generation models are penalized logP and quantitative estimate 2018; You et al., 2018; Shi et al., 2019; Zang & Wang, 2020; Luo et al., 2021e; Liu et al., 2021). However, as criticized by Coley (2020), Cieplinski et al. (2020), and Xie et al. (2020), optimization of these scores may not lead the discovery of useful drugs. For example, the top-scoring molecule found in terms of penalized logP in the state-of ofate-of-the-art model is a trivial long chain of the maximum number of carbons (Luo al., 2021c), since penalized logP prefers large molecules.
frug-likeness, (QED) (Jin et al.,

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OOD control HOOO
In-distribution.
Sim: 0.800
Nalve diffusion
Dg:
Sim:: 0.489
20 Noise
05 -10.2
(a1) GENTRL
(a2) Training set
MOOD-ID
Sim: 0.m.0.348
Exploration boundary
MOOD
high-propertt
(b1) MOOD (ours)
(b2) Training set
region
Figure 1: (Left) The molecules found by GENTRL (Zhavoronkov et al., 2019) and MOOD, and the most similar molecules to those from the training set. Unlike GENTRL, MOOD discovered novel molecule that is different from any training molecule with higher docking score than the top 0.01% of the training set. (Right) Illustration of the reverse-time diffusion process of MOOD. MOOD leverages the OOD-controlled diffusion to extend the exploration boundary and generate OOD samples in the low-density region, while using the property prediction network to guide the sampling process to the high-property region, thereby discovering molecules with desired target properties that lie beyond the training distribution. MOOD-ID is the variant of MOOD that only utilizes the property prediction network without the OOD control.
To overcome such limitation of conventional property objectives, a few recent works adopted the docking score, binding affinity score based on the three-dimensional simulation of a target protein and drug candidate (Cicplinski et al., 2020). However, using the docking score a sole metrie is still insufficient as a reasonable proxy for drug activity, since heavy molecules with high docking scores likely to be false positives due the dependency of the docking score molecular weights (Pan et al., 2003). Furthermore, real-world drug discovery involves searching for molecules that meet multiple requirements, for example, protein-ligante interactions, drru-likeneee and synthesizability.
Unfortunately, the poor explorability of most existing drug discovery methods makes it difficult to successfully accomplish the multi-objective tasks. As the number of chemical requirements increases, fewer molecules in the training set will satisfy the given constraints, and the optimization problem will become more difficult when trying to generate molecules that meet all the requirements. Thus, to generate high-scoring molecules with respect to multiple chemical properties, and further, that are applicable the real-world, we need method that can more effectively explore the chemical space.
To this end, we propose novel de novo drug discovery framework for generating OOD molecules, that are completely different from those in the training set, but nonetheless satisfy the given constraints. Specifically, we first propose a score-based generative model for OOD generation, by deriving a novel OOD-controlledd reverse-time diffusion process that can control the amount of deviation from the data distribution. However, since the naïve OOD generation can yield molecules that are chemically implausible, difficult to synthesize, and lacking desired properties, we further extend our framework to perform conditional generation for property optimization. Our Molecular Out-Of-distribuee Of-distribution Diffusion (MOOD) framework utilizes the gradient of a property prediction network to guide the sampling process to domains that are highly likely satisfy the given constraints, while leveraging the proposed OOD control to explore beyond the space of known molecules. MOOD is able to generate molecules that lie beyond the training distribution without additional computational costs, unlike existing methods (c.g., RL-based exploration methods).
We experimentally validate the proposed MOOD on the molecule optimization task, on which MOOD outperforms state-of-the-arr molecule generation methods by generating novel molecules with high docking scores while satisfying QED and synthetic accessibility (SA) conditions, demonstrating its ability to effectively explore the chemical space and find chemical optima of multiple requirements. Notably, MOOD discovered a novel molecule (Figure 1 (Left; bl)) with a higher docking score than the top 0.01 % of the training dataset. We summarize our contributions as follows:
We devise a novel score-based generative model for OOD generation, which overcomes the limited explorability of previous generative models by leveraging our proposed OOD-controllee reverse-time diffusion process that can control the amount of deviation from the data distribution.
We propose novel score-based generative framework for molecule optimization which leverages the gradients of the property prediction network to guide the generation process, while extending the exploration space with the OOD control.
We experimentally demonstrate that our proposed conditional OOD molecule generation frame- work can generate novel molecules that drug- synthesizable, and have high docking scores on five protein targets, outperforming existing molecule generation methods, and even discovering novel molecules that outscore the top molecules in the original dataset.
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2 RELATED WORK
Score-based generative models Score-based generative models learn to reverse the perturbation process from data to noise in order to generate samples from a given data distribution. Song & Ermon (2019) proposed to design the perturbation process with multiple noise scales, while Ho et al. (2020) proposed to consider the perturbation as a parameterized Markov chain, and Song et al. (2021b) united these approaches by generalizing the perturbation as a diffusion process modeled by a stochastic differential equation (SDE). Recently, score-based generative models have shown successful results for the generation of graphs (Niu et al., 2020; Jo et al., 2022), and arose as promising methods for molecular conformation generation (Shi al., 2021; Xu et al., 2022; Luo al., 2021b) and even 3D molecule generation (Hoogeboom et al., 2022). Yet, the application of score-based models for targeted de novo drug discovery poses a unique challenge not found in other domains: finding novel molecules that satisfy specific constraints in the vast chemical space. To the best of our knowledge, we are the first propose a score- based generative framework for molecule optimization.
Conditional score-based models Recently, score-based generative models have been applied to conditional generation tasks, such as image inpainting (Song al., 2021b), super-resolution (Choi et al., 2021; Li et al., 2022; Saharia et al., 2021), MRI reconstruction (Chung & Ye, 2021; Jalal et al., 2021: Song et al., 2021a), image translation (Meng et al., 2021; Sasaki et al., 2021), and point cloud generation (I.yu et al., 2021). However, directly adapting these schemes to molecule optimization is challenging, due to the complex dependency between nodes and edges which determines the chemical validity and properties of molecules. We introduce novel conditional reverse-time diffusion for controlled OOD generation, while using a property predictor to guide the sampling process, which together steers the generation to the intersection of low-density and high-property regions.
Molecule generation models Existing methods for generating molecular graphs of desired properties include models based variational autoencoders (VAEs) (Gómez-Bombarelli al., 2018; Jin et al., 2018; Liu et al., 2018; Eckmann et al., 2022), generative adversarial networks (GANs) (Lima Guimaraes et al., 2017: De Cao & Kipf, 2018), genetic algorithms (Jensen, 2019), and flow-base bow-based models (Shi et al., 2019; Zang & Wang, 2020; Luo et al., 2021c). A score- based graph generation model for unconditional molecule generation has been proposed recently (Jo et al., 2022). A common shortcoming of existing works that are based on distributional learning or fragment vocabularies is the limited exploration in the chemical space beyond the known data distribution, as they focus on interpolating the learned distribution or reassembling substructures of known molecules. Among the few works that consider docking score as the target property (Olivecrona et al., 2017; Jeon & Kim, 2020; Yang et al., 2021; Eckmann et al., 2022), Yang et al. (2021) focus on the exploration and RL objective to discover novel molecules. However, exploration of the agent is computationally expensive, and the method is inherently limited by the fragment vocabulary, which are the subgraphs of the seen molecules. Contrarily, our framework is able to generate novel molecules with desired properties outside the distribution of the training set, without requiring high computational costs or a fragment vocabulary.
proposed an
MOLECULE OPTIMIZATION WITH SCORE-BASED OUT-OF- GENERATION
In this section, we introduce our Molecular Out-Of--iitributiion Diffusion (MOOD) framework, which aims to generate molecules that are both novel with respect to the training data distribution and have desired chemical properties. We first present a novel OOD-controlled diffusion process that can explore beyond the training distribution in Section 3.1. Then, we describe our proposed MOOD based on a property- -uudedd sampling process with OOD-controlled diffusion in Section 3.2. We begin with the descriptions of molecular graphs and the score-based graph generation scheme.
3.1 SCORE-BASED OUT-OF-DISTRIBUTION GENERATION
Molecular graph representation A molecule can be represented as a molecular graph G (X, A) E NxP x NNN. :- G. where X is the node feature matrix carrying the information of the atom types described by F-dimensional one-hot encoding, A is the adjacency matrix representing the bond types, and N denotes the maximum number of heavy atoms (i.e., atoms besides hydrogen) of a molecule in the dataset. This representation directly uses the bond types (1 for single bonds, for double bonds, and 3 for triple bonds) as elements of A instead of the one-hot encoding.
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Score-based graph generation The seminal work of Song al. (2021b) models the diffusion from data to noise through a stochastic differential equation (SDE), and learns to reverse the process from noise to data. However, its naive extension to graph generation cannot model the complex dependency between nodes and edges, which is crucial for learning the distribution of graphs. To address this problem, Jo al. (2022) proposed Graph Diffusion via the System of SDEs (GDSS), which models the diffusion of both the node features and the adjacency matrix with system of SDEs. Specifically,, the forward diffusion for graph {G. = (X,, A.)) is defined by Itô SDE:
dG. f,(G,) + gıdw;
with the linear drift coefficient f.(:): - G' the scalar diffusion coefficient gr: G R. and the standard Wiener process w. Denoting the marginal distribution under the forward diffusion as Pt, the corresponding reverse diffusion process can be described by the following system of SDEs:
dxx; = (X,, - o.. V log Ps Xx A.) dt + +1,:dW1
(2)
[AA, = (A.) g3.t V A. log X A+) di + 92,rdW2,
where G,(X, A) = (X), (A)) and Sr (g),,, 92.z) are the drift and diffusion coefficients, respectively, W1 and W2 are the reverse-time standard Wiener processes, and di is an infinitesimal negative time step. The score networks 80,.t and 80,.t are trained to approximate the partial score functions V x. log (X,, A,) and V A. Po P r, At), respectively, then used to simulate Eq. (2) backwards in time to jointly generate the node features and the adjacency matrices.
Although GDSS can generate high-quality molecular graphs that follow the data distribution, it is not free from the explorative limitation of deep generative models described in Section 1. To tackle this limitation, introduce novel based OOD generative model.
Exploration with OOD control a novel OOD-controlled score-based graph generative model that can generate samples outside in-distribution, where the OOD-ness of the generative process is controlled by the hyperparameter E [0, 1). We approach by sampling from the conditional distribution pr pr = A) where yo represents the OOD condition, by solving the following conditional reverse-time SDE:
To expand the exploration space of the diffusion, we propose
dG, [G.) o. V., log (G.ly. ^)] dt + g.dw.
The conditional score log (G.ly. A) can be decomposed as the sum of the two gradients:
VG, logg A) Vc, log VG, logp: A|Gr),
(4)
and since the score function VG, logp: (Gt) can be estimated by the score networks se,, and sp,.t. simulating Eq. (3) is possible if the second term is known. In order to access VG, log P = A G. exploit the fact that the OOD samples are the ones of low-likelihood with respect to the in- distribution (Du & Mordatch, 2019; Grathwohl et al., 2020). Specifically, we propose to model the distribution pr >\G:) to be proportional the negative exponent of the density (G,))
Prly. = A/.)) pe. 1
where H, (G, I (G. p.) and p. is the probability threshold. The existence of such distribu- tion is shown in Section A. of the appendix.
Based on the modeling of Eq. (5), derive novel con-controlled reverse- time diffusion process from Eq. (3) as follows (see Section A.2 of the appendix for the detailed derivation):
dG. [f.(G.) (1 vX)g V (o:)
g.dw.
Intuitively, as À approaches 1, the distribution py = X A/G.) modeled by Eq. (5) becomes sharper since the negative exponent induces larger magnitude for smaller probability values, which amplifies the effect the OOD condition. Accordingly, the influence of the score VG, log (G,)) in the drift coefficient weakens, and the sampling process is guided to the lower density regions.
"t-sbbccript is used to represent function time: F+(-) == F() and Mo.(-) = Mo(-t). We empirically found that using vX instead of yields well-scaled results as the value of À changes.
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Looking from the perspective of the reverse-time diffusion process. Eq. (6) induces a marginal distribution proportional to pt (G,)1-VX, Consequently, simulating the OOD-controlled diffusion process backward in time generates samples from the relatively uniform distribution compared to the original data distribution, where the dispersion is controlled by A, and the corresponding samples are more likely to come from outside the in-distribution. Therefore, the proposed OOD-controlled diffusion process of Eq. (6) can be used as an OOD generative model that can control the deviation from the data distribution with the hyperparameter X. Notably, the OOD control enables to explore further from the data distribution without additional computational costs, in contrast to previous molecule generation methods (Olivecrona al., 2017; Jeon & Kim, 2020; Yang al., 2021) that rely on costly reinforcement learning algorithms for exploration.
We empirically demonstrate that the proposed OOD- diffu- sion process is indeed able to control the OOD-ness of the generated samples on simple Gaussian mixture in Figure 2. While the OOD control with X = 0 (i.e., GDSS) accurately generates samples from the data distribution, we can generate a wide scope of OOD samples by simply increasing the hyperparameter X.
2=
However, being able to generate OOD molecules does not necessarily mean that we will be able to discover useful molecules, since they may be chemically implausible, difficult to synthesize, or have low affinity to target protein. Thus, for the OOD generator to be truly useful, should conditionally generate molecules that satisfy certain desired conditions, which we describe in Section 3.2.
1=0.5
2=0.9
Figure 2: A toy experiment on the OOD-controlled diffusion.
3.2 MOLECULE PROPERTY OPTIMIZATION
Property optimization with conditional generation Our goal is generate novel molecules that possess desired chemical properties, for example, high binding affinity against a target protein.
represent the condition of maximizing certain property as Yp: our objective then is to generate molecules from the conditional distribution Pe (G.l.. = Xp).. which can be decomposed as follows:
Pr (G.y. = X,) (G.) Pr A/G.) pelyp = A)
(7)
Since pypplGr y. A) represents the probability that the molecular graph G. satisfies the property yp, we propose to model the probability density using the Boltzmann distribution as follows:
Pt (y Gt. = >) = Po(G,A) /Zi,
(8)
where is the scaling coefficient, Z, is the normalization constant, and Po is the property function estimated by a property prediction network, which we describe in detail at the end of this section.
Using Eq. (5) and Eq. (8), we propose a novel conditional reverse- time diffusion process for generating OOD molecules that satisfy specific constraints as follows:
dG. = f. (G.) - (1- - V VG, logp:(G.)) - a.g, VG, Po di + g: (9)
which refer to as Molecular Out- df-diitribttion Diffusion (MOOD). Figure (Right) illus- trates the generation process of MOOD, where the additional gradients v vng G log (G.)) and X) of Eq. (9), that are not in the unconditional process of Eq. (2), can be under- stood the guidance that drive the sampling process to the low-density regions and the high-property regions, respectively. However, Fq. (9) cannot be directly used as a generative model since it does not model the node-edge relationships (Jo et al., 2022), and thus utilize the equivalent diffusion process through the system of reverse-time SDES as follows:
dxx, (X.) - (1 Viggi. 86, (X,, A.) an. V P. Po, Ac, (c, A) dt + +g.
(10)
dAA, (2) vD)g.. 802. (X, At) 02. V.. Pa A) di + 92.
To balance the effect of the OOD control and the property gradient, we propose automatically set a1ee and a2, throughout the diffiusion according to a predetined ratio between the magnitudes of the partial scores and the property gradients as follows:
||s0, (G.)l
1892 (G.)l
01 = Fi
|
(G,, : 022, = r2,
|V Pa (G., XII
(11)
where ri, and F2 are the time-dependent magnitude ratios and ||. || is the entry-wise matrix norm.
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ZINC250K
A=0
1=0.110
A=0.15
95
30
Novellty (14
900
FCD
20
85
(a)
(b) (c)
(d)
0.100.15
0.10
0.15
75
0.100.15
Figure 3: (Left) UMAP visualization of the ZINC250K dataset and the generated molecules by the proposed OOD-controlled diffusion process. Each point represents a molecule based on the activation of the CetmNet layer. (Right) Evaluation results of the molecules generated by the OOD-controlled diffusion. We report FCD, NSPDK MMD, and novelty of the generated molecules with various values of the hyperparameter A.
Property prediction network To approximate the property function of the desired property, train a property prediction network P& to estimate the property of a given molecule Gy. Since chemical properties are entirely determined by molecules, Pa can predict the target property without A, and we utilize the architecture of the discriminator network of De Cao & Kipf (2018) as follows:
(G,) = MLP, MLP,,tanhl (tanh(HH)) for H' MLP, (10)) @ MLP, (((H)))=0)),
(12)
where H;-1 tanh( GNN (N, with graph convolutional network (GCN) (Kipf & Welling, 2017) as the GNN and Ho = =X,, L is the number of the GNN operations, MLP, and MLP, are the multilayer perceptrons (MLPs) with sigmoid and tanh activation functions, respectively, @ is the element-wise multiplication, and [-] is the concatenation operation.
EXPERIMENTS
We first validate the efficacy of our OOD-controlled diffusion process novel molecule generation task in Section 1, then demonstrate the effectiveness of MOOD on property optimization tasks in Section 4.2. We further conduct an ablation study to verify the effectiveness of MOOD's 's individual components in Section 4.3.
4.1 NOVEL MOLECULE GENERATION
Experimental setup To verify that our proposed OODD-contolledd diffusion scheme can control the OOD-ness of the generated samples and enhance the explorability, we first conduct an experiment on an unconstrained novel molecule generation task. We generate 3,000 molecules without incorporating the property network (i.e., Eq. (6)), varying the hyperparameter À for OOD control. We measure the O0D-ness of the generated molecules with respect the training dataset, ZINC250K (Irwin et al., 2012), using the following metrics. Fréchet ChemNet Distance (FCD) (Preuer et al., 2018) is the distance between the training and generated set of molecules based on the activations from the penultimate layer of ChemNet. Neighborhood subgraph pairwise distance kernel maximum mean discrepancy (NSPDK MMD) (Costa & De Grave, 2010) is the MMD between the test set and the generated set. Novelty (Jin et al., 2020b; Xie et al., 2020) is the fraction of valid molecules that have a similarity less than 0.4 with the nearest neighbor in the training set.
Results We visualize the distribution of the generated molecules via two-dimensional uniform man- ifold approximation and projection (UMAP) (McInnes & Healy, 2018) in Figure 3 (Left). We observe that the proposed OOD-controlled diffusion scheme not only enables to generate OOD molecules, but also allows the deviation from the training dataset to be controllable with the hyperparameter the value of X increases, the sampling space deviates more from the training distribution. We further quantitatively measure the OOD-ness of the generated molecules in Figure 3 (Right). Similarly, as À increases, FCD and NSPDK MMD increase, which shows that the distribution of generated molecules becomes more different from the training distribution in the view of biochemical activity and molecular graph structures. Notably, larger À increases novelty well, indicating that each generated molecule is indeed comprised of chemically distinct substructures from the seen molecules.
As
4.2 PROPERTY OPTIMIZATION
Experimental setup The goal of the property optimization task is to generate novel molecules that are high binding affinity, drug-like, and synthesizable. To reflect these constraints, we accordingly construct the property function Parj as follows:
Pory DS, QED(G.) SA(G.) e [0, 1),
(13)

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Table I: Novel hit ratio (%) results. The results are the means and the standard deviations of 5 runs. The best performance and comparable results (p > 0.05) are highlighted in bold.
Target protein
Method
papl
fa7
5htlb
braf
jak2
REINVENT (Olivecrona al. 2017)
0,480 0.344)
0.213 (= 0081)
2,453 0.561)
0.127 o.88))
0.613 (= 0.167)
JTVAE (Jin et al., 2018)
0.856 (= 0.211)
0.289 [ 0.16)
4.656 (1: 1.405)
0.144 (4 0.068)
0.815 (:: 0.044)
GraphAF (Shi
2019)
0.689 0116))
0.011
0316)
3.178
(# 0.393)
0.956
0.319)
0.767 0.098)
HierVAE (Jin et al., 2020a)
0.553 0.214)
0.007
t= 0.013)
0.507
(4 0.278)
0.207
(4 0.230)
0.227 (s: 0.127)
GraphDF (Luo el al., 202
0.044 0.031)
0.000
0.000)
0.000
0.000)
0.01 (2:06))))
0.011
FREED (Yang et al., 2021)
3.627 (296))
1.107 0:20))
10.187
(#: 3.909)
2.067
(= 0.626)
4.520 (= 0.67))
FREED-QS
4.627 0.727)
1.332 0:113)
16,767
(1.089))
2.940 0.359)
5,800 0.295)
LIMO (Fickmann et al., 2022)
0.455 (= 0.057)
0.044
(= 0.016)
1.189
(2: 0.10)
0.278
(=: 0.134)
0.689
(= 0.319
GDSS (Jo ct al., 2022)
1,933
0,368
4,667
0.167
1.167
MOOD-wlo Ps (ours)
2.127 0.216)
0,447
0J91)
7.900 (# 0.455)
0,520
0.117)
2.293
0.223)
MOOD-ID (ours)
3,400 (L. 0,117)
0,433 (1 0.063)
11.873 (1 0.521)
2.207
(1 0.165)
3,953 0.383)
MOOD (ours)
7.017 0.428)
0.733
18.673 0.423)
5,240 0.285)
9.200 0.524)
Table 2: Novel top 5% docking score (kcal/mol) results. The results are the means and the standard deviations of 5 runs. The best performance and comparable results (p > 0.05) are highlighted in bold.
Target protein
Method
parp1
Shilb
braf
jak2
REINVENT (Olivecrona et al., 2017)
-8.702 (= 0.523)
-7.205
0,264)
-8.770 ct: 0.316)
-8,392
0.400)
-8.165 0:277)77)
JTVAE (Jin 2018)
-9.482 (= 0.122)
-7.683
(=t 0.048)
-9.382 (#: 0.332)
-9.079
(:: 0.069)
-8.885
(4: 0.025)
GraphAF (Shi et 20199
-9.327
(= 0.30)
-7.084
cz 0.025)
-9.113
(t: 0.36
-9.896
(t: 0.226)
-8.267
(#:0.101)
VierVAE (Jin 2020a)
-9.487
02200
-6.812
0.224
-8.081
-8.978
-8.285
0.500
GraphDF (Luo et al., 2022c))
-6.823 tz 0.154)
-6.072
(#: 0.081)
-7.090
(2: 0.100)
-6,852
(:: 0.318)
-6.759
(1: 0.111)
FREED (Yung al., 2021)
-10.427 Li: 0.177)
-8.297
0,084)
-10.425
0:311)
-10.325
0.164)
-9.624 0.10.0
FREED-QS
-10.579 (= 0.104)
-8.378
0.044)
-10.714
(#: 0.183)
-10.561
0.080)
-9.735 0.022)
LIMO (Eekmaann et al., 2022)
-8.984 ta 0.227)
-6. 764
cá 0,142)
-8,422
(1: 9.865)
-9.046
t:: 0,316)
-8.435
(4) 0,273)
GDSS (Jo et al.. 2022)
-9,967 0.228)
-7.775
-9.459
(+:
-9,224
-8,926
0.089)
MOOD-w/o Pa (ours)
-1.0866 (z: 0.33))
-7.9 7,932
(#t 0,054)
-9.838
(#: 0.053)
-9.634
ta: 0.052)
-9.247 (#: 0,041)
MOOD-ID (ours)
-104009 (= 0.30)
-7. -7.947
0.084)
-10.487
(t: 3.089)
-10.421
-9.575
(t 0.075)
MOOD (ours)
-10.865 (=: 0.113)
-8.160
(# 0,071)
-11.145
(# 0.042)
-11.66
(#: 0.034)
-10.147
(4: 0.060)
where DS is the normalized docking score (DS), QED is the drug- and SA is the normalized synthetic accessibility (SA). We train the property network Ps to predict the property value Par; of the molecules in the ZINC250K dataset. Previously used metrics for evaluating docking-optimizer molecules. such as hit ratio or the average of the top 5% DS (Yang et al., 2021) are insufficient for de novo drug discovery, as they do not consider whether the generated molecules are novel or not, Therefore, we evaluate 3,000 generated molecules with the following metrics. Novel hit ratio (%) ) is the fraction of unique hit molecules that have the maximum Tanimoto similarity less than 0.4 with the training molecules. Here, hit molecules are defined as the molecules that satisfy the following constraints: DS (the median DS of the known active molecules), QED > 0.5, and SA <5. Novel top 5% docking seore is the average DS of the top 5% unique molecules that satisfy the constraints QED 0.5 and SA < 5 and have the maximum similarity less than 0.4 with the training molecules. Note that these metrics jointly evaluate novelty and multiple properties, thereby more suitable for real-world scenarios. We use five protein targets, parp1, fa7, Shtlb, braf, and jak2.
Baselines REINVENT (Olivecrona et al., 2017) is an RL model that utilizes prior sequence model. JTVAE (Jin et al., 2018) is a VAE-based model that utilizes the junction tree molecular representation and Bayesian optimization. GraphAF (Shi et al., 2019) and GraphDF (Luo et al., 2021c) are flow-based models that utilize continuous and discrete latent variables, respectively. HierVAE (Jin al., 2020a) is VAE-based model that utilizes hierarchical molecular representation and active learning. FREED (Yang et al., 2021) is a fragment- based RL model that utilizes prioritized experience replay (PER) (Schaul et al., 2015) for exploration, and FREED-QS is our modification of FREED that exploits Pary of Eq. (13) as its reward function. LIMO (Fekmann et al., 2022) is VAE-based model that generates molecules with an inceptionism-lik technique. We also compare with GDSS (Jo et al., 2022), MOOD-w/o Pg. MOOD that only utilizes the OOD exploration without the property prediction network by setting T1, = T2, = O, and MOOD-ID, MOOD that only utilizes the property prediction network without the OOD exploration by setting X = 0.
Results As shown in Table and Table 2, our proposed MOOD significantly outperforms all the baselines for most of the target proteins, and shows competitive results on fa7 compared to FREED and FREED-QS. The performance gap shown in the novel hit ratio and the novel top 5% DS indicates that MOOD is superior in discovering novel molecules that are drug-like, synthesizable, and have a high binding affinity. Notably, MOOD consistently outperforms MOOD-ID for all the target proteins,
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ZINC250k
REINVENT
FREED-QS
MOOD-ID
MOOD
30
NSPDK (x1e-)
(a)
(b)
(d)
Figure 4: (Left) UMAP visualization of the molecules from ZINC250K and the generated samples with parpl
as the target protein. See Figure 5 for the symbols depicted in (c) and (d). (Right) Distributional distances of
the generated molecules measured by FCD and NSPDK MMD with respect to ZINC250K.
REINVENT
HierVAE
FREED-QS
MOOD-ID
MOOD
ZINC250K Generated
Sim: 0.717 0S:110.1
Sim: O 567 / DS: 10.7
Sim: 0.679/ DS: -10.7
Sim: 0.489/ DS: -1.2
Sim: 0 ..348 DDS-1108
A
Figure 5: Generated hit molecules with parpl as the target protein and the corresponding ZINC250K molecules of the highest similarity. The similarity and docking score (kcal/mol) are provided at the bottom of each generated hit. The molecules with symbols are the ones marked in Figure 4 (c) and (d).
and MOOD-w/o Pa also consistently outperforms GDSS even without the aid of property gradient, together demonstrating that the proposed exploration via OOD generation is highly effective in finding novel chemical optima of multiple constraints. We further provide the results of novelty, diversity, uniqueness, hit ratio, and top 5% DS in Table 9, Table 10, Table 11, Table 12, and Table 13 of Section D.2, respectively. As shown in these tables, the OOD control utilized in MOOD largely enhances novelty while maintaining near-pers car-perfect uniqueness compared to MOOD-ID. Moreover, the improved exploration over MOOD-ID also aids MOOD terms of hit ratio and top 5% DS, as is able to discover molecules with better properties outside the data distribution.
Explorability We visualize the distribution of the generated molecules via UMAP in Figure (Left). As shown in the figure, MOOD exhibits superior explorability beyond the training distribution compared to the baselines. While the generated molecules of REINVENT and FREED-QS lie close the ZINC250K molecules, most of the generated molecules of MOOD lie beyond the training distribution. Note that MOOD-ID generates some molecules that deviate from the training distribution by the effect of the property gradient in its diffusion, yet the fraction is smaller than those of MOOD due to the lack of the OOD constraint. We further measure the distributional distance of the generated molecules from ZINC250K via FCD and NSPDK MMD Figure (Right). Together with the high novelty shown in Table 9 of Section D.2, the results verify that MOOD is able to generate novel molecules that are significantly different from those of the training dataset.
Generated molecules We visualize the generated molecules of MOOD and the baselines in Figure 5 and Figure of Section D.3. As shown in the figures and also in Table 9 of Section D.2, the molecules generated by the baselines possess duplicated substructures with the ZINC250k molecules due the limited explorability and accordingly have high maximum Tanimoto similarity and low novelty. This limits their application to de novo drug discovery. In contrast, the generated molecules of MOOD exhibit low similarity with the ZINC250K molecules, while having high binding affinity. As shown in Figure 4, the molecule found by MOOD in Figure 5 indeed an OOD sample, that lies outside the training distribution, unlike the one found by MOOD-ID.
MOOD
ZINC250K
Discovery with MOOD To validate that MOOD can find novel chemical optima that lie beyond the training distribution with even better chemical properties, we visualize the hit molecules found by MOOD that have higher binding affinity to parpl than those of the top 0.01% of ZINC250k Figure 6. Note that the molecules also have low similarity with the molecules of ZINC250k. This result suggests the applicability and efficacy of MOOD in real-world de novo drug discovery.
13.5 0.278
13.0
DS: 12.8 Sim: 0.14 Figure 6: Novel hit molecules found by MOOD against parpl and the top 0.01 % ZINC250K molecules.
DS. -12A
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Table 3: Novel hit ratio (%) and novel top 5% docking score (keal/mol) results with 3D molecule generation baselines and GDSS with respect the target protein glmu. Results are the means and the standard deviations 5 runs. Best performance and its comparable results (p > 0.05) are highlighted in bold.
Top 5% DS (kcal/ (kcal//ml)
Method
Novel hit ratio
Novel top 5% DS
Luo et al. (2021a)
1.367 (4: 1.24)
-6.328 (= 0.567)
Pocker2Mol (Peng et al., 2022)
6.002 (t 0.93)
-7.714
(= 0.123)
Lower half L-MOOD-I L-MOOD
GDSS (Jo et al., 2022)
1.227 (:: 0.100)
-6.411
(= 0.046)
Figure 7: Top 5% docking score dis- tribution of the molecules with respect to the target protein parp1. Each of the horizontal lines represents the average value of the distribution.
MOOD-w/o Po (ours)
7.320 0.404)
-7.673
0.069)
MOOD-ID (ours)
10.453 1.81))
-7.832
(= 0.169)
MOOD (ours)
16.733 1,984)
-8.423 0.164)
Comparison with 3D molecule generation methods We additionally compare MOOD with the methods of a recently emerging area, namely, three-dimensional (3D) molecule generation. The model of Luo et al. (2021a) and Pocket2Mol (Peng et al., 2022) are autoregressive models that generate molecules of high binding affinity by utilizing 31) information of the binding site of the target protein. As shown in Table 3, MOOD largely outperforms the baselines even without the spatial information of the binding pocket, again confirming that MOOD is highly practical and has great potential in solving real-world drug discovery problems.
4.3 ABLATION STUDY
Effects of the OOD control and property gradient To examine the effect of the proposed OOD control and property gradient, we compare MOOD-w/o Po. MOOD-ID and MOOD with GDSS. As shown in Table 1, Table 2, and Table 3, using both the OOD generation scheme and the guidance from the property prediction network essential for finding better chemical optima. Specifically, the superior generation result of MOOD over MOOD-w/o Pa and MOOD-ID over GDSS demonstrate the effectiveness of the property gradient, while the superiority of MOOD over MOOD-ID and MOOD-w'o Po over GDSS demonstrate the effectiveness of the OOD control.
Training on the low-property subset To further validate the explorability of the proposed MOOD, we evaluate the generated molecules of L-MOOD-ID and L-MOOD, which are respectively MOOD- ID and MOOD trained on the lower half subset of the ZINC250K dataset in terms of Parj (Bq. (13)). We visualize the distribution the top 5% DS of the molecules that satisfy QED > 0.5 and SA < in Figure 7. We first observe that both L-MOOD-ID and L-MOOD yield higher top 5% DS compared to their training set, demonstrating the effectiveness the proposed conditional diffusion process with the property prediction network. Furthermore, unlike L-MOOD-ID, L-MOOD is able generate molecules with higher top 5% DS compared to the original ZINC250K dataset, even though L-MOOD has never seen the molecules the higher half of ZINC250K. This shows that exploring beyond the known chemical space with MOOD is not only beneficial for novel molecule discovery, but also for property optimization since the novel molecules may better satisfy the given properties.
CONCLUSION
To tackle the limited explorability of previous molecule generation models, we proposed Molecular Dui-Ot-distribution Diffussion (MOOD), new score-based generative model for generating novel molecules with desired chemical properties outside the training distribution. MOOD leverages novel OOD-controlled reverse-ting timse diffusion process that can control the OOD-ness of the generated samples without any additional costs. MOOD further incorporates a novel conditional score- based diffusion scheme to optimize molecules for target chemical properties, using the gradient of the property prediction network to guide the diffusion process to the high-propen MOOD on the multi-objective property optimization tasks that are analogous real-world drug discovery scenarios, on which ours outperforms existing molecular generation methods with superior explorability and property optimization performance. Further, method generated novel molecules that are largely different from any of the existing molccules in the training set, showing its potential promising means of de novo drug discovery.
regions. We validated
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REPRODUCIBILITY STATEMENT
Code. We provide the codebase construct MOOD and conduct the experiments in the paper as the supplementary file.
Datasets. We use ZINC250K (Irwin et al., 2012) and CrossDocked2020 (Francoeur et al., 2020) for the experiments.
Toy experiment. We provide the details of the toy experiment of Figure Section C.I.
Novel molecule generation. We provide the details of the novel molecule generation experiment of Figure 3 in Section C.3.
Property optimization. We provide the details of the property optimization experiment of Table 1, Table 2, Figure 4, Figure 5, Figure 6, and Figure 7 in Section C.4. The details of the property optimization experiment Table 3 with the CrossDocked20200 dataset are also provided in Section C.4.
REFERENCES
Amr Alhossary, Stephanus Daniel Handoko, Yuguang Mu, and Chee-Keong Kwoh. Fast, accurate, and reliable molecular docking with quickvina Bioinformatics, 31(13):2214-22) 2015.
Jooyoung Choi, Sungwon Kim, Yonghyun Jeong, Youngjune Gwon, and Sungroh Yoon. ILVR: conditioning method for denoising diffusion probabilistic models. In 2021 IEEE/CVF International Conference on Computer Vision, ICCV 2021, Montreal, QC, Canada, October 10-17, 2021, pp. 14347-14356. IEEE, 2021.
Hyungjin Chung and Jong Chul Ye. Score-based diffusion models for accelerated MRI. ar.:v:2110.05243, 2021.
Tobiasz Cieplinski, Tomasz Danel, Sabina Podlewska, and Stanislaw Jastrzebski. We should least be able to design molecules that dock well. arXiv preprint arXiv:2006. 16955, 2020.
Connor Coley. Defining and exploring chemical spaces. Trends in Chemistry, 2020.
Fabrizio Costa and Kurt De Grave. Fast neighborhood subgraph pairwise distance kernel. In Proceedings of the 26th International Conference on Machine Learning, pp. 255-262. Omnipress; Madison, WI, USA, 2010.
Nicola De Cao and Thomas Kipf. Molgan: An implicit generative model for small molecular graphs. ICML 2018 workshop on Theoretical Foundations and Applications of Deep Generative Models, 2018.
Yilun Du and Igor Mordatch. Implicit generation and modeling with energy based models. In Hanna M. Wallach, Hugo Larochelle, Alina Beygelzimer, Florence d' Alché-Bue, Emily Fox, and Roman Garnett (eds.), Advances in Nearal Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, December 8-14, 2019, Vancouver, BC, Canada, pp. 3603-3613, 2019.
Peter Eckmann, Kunyang Sun, Bo Zhao, Mudong Feng, Michael K Gilson, and Rose Yu. Limo: Latent inceptionism for targeted molecule generation. In Proceedings of the 39th International Conference on Machine Leurning, 2022.
Paul G Francoeur, Tomohide Masuda, Jocelyn Sunseri, Andrew Jia, Richard B lovanisci, Ian Snyder, and David R Koes. Tiree-dimensional convolutional neural networks and cross-docked data set for structure-based drug design. Journal of chemical information and modeling, (0(9):4200-4211 2020.
Miguel Maaría-Orrteóón Gregor NC Simm, Austin J Tripp,, José Miguel Hernández-Looato Andreas Bender, and Sergio Bacallado. Dockstring; easy molecular docking yields better benchmarks for ligand design. Journal of chemical information and modeling, 62(15):346--3002 2022.
Rafael
David Duvenaud, José Miguel Hernández-Lobato, Jorge Aguilera- Iparraguirre, Timothy D. Hirzel, Ryan Adams, and Alán Aspuru-Guzin Automatic chemical design using data-driven continuous representation of molecules. arXiv: 1610.026// 2016.
10

---

Under review as a conference paper at ICLR 2023
Rafael Komez-Bombarrele Jennifer N Wei, David Duvenaud, José Miguel Hernández-Lobato, Benjamín Sánchez- Sánchez-Lengehe Lengeling, Dennis Sheberla, Jorge Aguilera-Iparann Iparraguirre Timothy D Hirzel, Ryan P Adams, and Alán Aspuru-Guzik. Automatic chemical design using data-driven continuuus representation of molecules. ACS central science, (2):268-2766 2018.
Will Grathwohl, Kuan-Chich Wang. Jömn-Herik Jacobsen, David Duvenaud, Mohammad Norouzi, and Kevin Swersky. Your classifier is secretly an energy based model and you should treat it like one. In 8th International Conference on Learning Representations, ICLR 2020. Addis Ababa, Ethiopia, April 26-30, 2020. OpenReview.net, 2020.
Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. In NeurIPS, 2020.
Emiel Hoogehoom, Victor Garcia Satorras, Clément Vignac, and Max Welling. Equivariant diffusion for molecule generation in 3d. arXiv:2203.17003: 2022.
John J Irwin, Teague Sterling, Michael M Mysinger, Erin S Bolstad, and Ryan G Coleman. Zinc: free tool discover chemistry for biology. Journal of chemical information and modeling, 52(7): 1757-1768, 2012.
Ajil Jalal, Marius Arvinte, Giannis Daras, Eric Price, Alexandros G. Dimakis, and Jonathan I. Tamir. Robust compressed sensing MRI with deep generative priors. arXiv:2108.01335 2021.
Jan H Jensen. A graph-based genetic algorithm and generative model/monte carlo tree search for the exploration of chemical space. Chemical science, 10(12):3567-3572, 2019.
Woosung Jeon and Dongsup Kim. Autonomous molecule generation using reinforcement learning and docking develop potential novel inhibitors. Scientific Reports, 10, 12 2020.
Wengong Jin, Regina Barzilay, and Tommi Jaakkola. Junction tree variational autoencoder for molecular graph generation. In International Conference on Machine Learning, pp. 2323-2332. PMLR, 2018.
Wengong Jin, Regina Barzilay, and Tommi Jaakkola. Hierarchical generation of molecular graphs using structural motifs. In International Conference on Machine Learning, pp. 4839-443444 4848. PMLR, 2020a.
Wengong Jin, Regina Barzilay, and Tommi Jaakkola. Multi-objective molecule generation using interpretable substructures. In International Conference on Machine Learning, pp. 1849-4859) PMLR, 2020b.
Jachyeong Jo, Seul Lee, and Sung Ju Hwang. Score-based generative modeling of graphs via the system stochastic differential equations. In Proceedings of the 39th International Conference on Machine Learning, 2022.
Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.69886 2014.
Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings. 2017.
Matt J Kusner, Brooks Paige, and José Miguel Hernández- Grammar variational autoencoder. In International Conference on Machine Learning, pp. 1945-1954. PMLR, 2017.
Greg Landrum et al. Rdkit: Open-source cheminformatics software, 2016. URL http://www: rdkit. org/. https://github. com/rdkit/vdkii, 2016.
Haoying Li, Yifan Yang, Meng Chang, Shiqi Chen, Huajun Feng. Zhihai Xu, Qi Li, and Yueting Chen. Srdiff: Single image super-resolution with diffusion probabilistic models. Neurocompating, 479:47-59, 2022.
Jaechang Lim, Seongok Ryu, Jin Woo Kim, and Woo Youn Kim. Molecular generative model based on conditional variational autoencoder for de novo molecular design. J. Cheminformatics, 10(1): 31:1-31:9, 2018.
11

---

Under review as a conference paper at ICLR 2023
Gabriel Lima Guimaraes, Benjamin Sanchez-Lengeling Carlos Outeiral, Pedro Luis Cunha Farias, and Alín Aspuru-Guzik, Objective-reinforeed generative adversarial networks (organ) for sequence generation models. arXiv, pp. arXiv-1705, 2017.
Meng Liu, Keqiang Yan, Bora Oztekin, and Shuiwang Ji. Graphebm: Molecular graph generation with energy-based models. In Energy Based Models Workshop-ICLR 2021, 2021.
Qi Liu, Miltiadis Allamanis, Marc Brockschmidt, and Alexander Gaunt. Constrained graph variational autoencoders for molecule design. In Proceedings of the 32nd International Conference on Neural Information Processing Systems, pp. 7806-7815, 2018.
Shitong Luo, Jiaqi Guan, Jianzhu Ma, and Jian Peng. A 3d generative model for structure- drug design. Advances Neural Information Processing Systems, 04:6229-6239, 2021a.
Shitong Luo, Chence Shi, Minkai Xu, and Jian Tang. Predicting molecular conformation via dynamic graph score matching. In Thirty-Fifit Conference on Neural Information Processing Systems, 2021b.
Youzhi Luo, Keqiang Yan, and Shuiwang Ji. Graphdf: A discrete flow model for molecular graph generation. International Conference on Machine Learning, 2021c
Zhaoyang Lyu, Zhifeng Kong, Xudong Xu, Liang Pan, and Dahua Lin. A conditional point diffusion- refinement paradigm for 3d point cloud completion. CoRR, abs/21 2021.
Leland McInnes and John Healy. UMAP: uniform manifold approximation and projection for dimension reduction. wrXiiv:802.034/4 2018.
Chenlin Meng, Yang Song, Jiaming Song, Jiajun Wu, Jun-Yan Zhu, and Stefano Ermon. Sdedit: Image synthesis and editing with stochastic differential equations. CoRR, 0ts/2108.01073 2021.
Chenhao Niu, Yang Song, Jiaming Song, Shengjia Zhao, Aditya Grover, and Stefano Ermon. Permu- tation invariant graph generation via score- based generative modeling. In AISTATS, 2020.
Marcus Olivecrona, Thomas Blaschke, Ola Engkvist, and Hongming Chen. Molecular de-novo design through deep reinforcement learning. Journal of cheminformatics, 9(1):1-14, 2017.
Yongping Pan, Niu Huang, Sam Cho, and Alexander D. MacKerell Jr. Consideration of molecular weight during compound selection in virtual target-based database screening. Chem. Inf. Comput. SSci,, 43(1):267-27,, 2003.
Xingang Peng, Shitong Luo, Jiaqi Guan, Qi Xie, Jian Peng, and Jianzhu Ma. Pocket2mol: Efficient molecular sampling based on 3d protein pockets. In Proceedings of the 39th International Conference on Machine Learning, 2022.
Kristina Preuer, Philipp Renz, Thomas Unterthiner, Sepp Hochreiter, and Gunter Klambauer. Fréchet chemnet distance: metric for generative models for molecules in drug discovery. Journal of chemical information and modeling, (799):173-17440 2018
Raghunathan Ramakrishnan, Pavlo O Dral, Matthias Rupp, and O Anatole Von Lilienfeld. Quantum chemistry structures and properties of 134 kilo molecules. Scientific data, 1(1):177, 2014.
Chitwan Saharia, Jonathan Ho, William Chan, Tim Salimans, David J. Fleet, and Mohammad Norouzi. Image super-resolution via iterative refinement. arXiv:2104.07636, 2021.
Hiroshi Sasaki, Chris G. Willcocks, and Toby P. Breckon. UNIT-DDPM: unpaired image translation with denoising diffusion probabilistic models. arXiv:2104.05358, 2021.
Tom Schaul, John Quan, Ioannis Antonoglou, and David Silver. Prioritized experience replay. arXiv preprint ar arXiv: wtw.::::511.09900 2015.
Daniel Schwalbe-Kode and Rafacl Gömez-Bombarelli. Generative models for automatic chemical design. arXiv:190.001332 2019.
Vikash Schwag, Caner Hazirbas, Albert Gordo, Firat Ozgenel, and Cristian Canton-Ferrer. Generating high fidelity data from low-density regions using diffusion models. arXiv:2203.1 222. 2022.
12

---

Under review as a conference paper at ICLR 2023
Chence Shi, Minkai Xu, Zhaocheng Zhu, Weinan Zhang, Ming Zhang, and Jian Tang. Graphaf: flow-based autoregressive model for molecular graph generation. In International Conference on Learning Representations, 2019.
Chence Shi, Shitong Luo, Minkai Xu, and Jian Tang. Learning gradient fields for molecular conformation generation. In Proceedings of the 38th International Conference on Machine Learning, JCML 2021, 18-24 July 2021, Virtual Event, volume 139 of Proceedings of Machine PMLR, 2021.
Learning Research, pp.
Yang Song and Stefano Ermon. Generative modeling by estimating gradients of the data distribution. In NeurlPS, 2019.
Yang Song. Liyue Shen, Lei Xing, and Stefano Ermon. Solving inverse problems in medical imaging with score-based generative models. arXiv:2111.08005 2021a.
Yang Song. Jascha Sohl-Dickstein Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. In ICLR, 20.lb.
W Patrick Walters and Mark Mureko. Assessing the impact of generative ai on medicinal chemistry. Nature Biotechnology. 38(2):143-145 2020.
Yutong Xie, Chence Shi, Hao Zhou, Yuwei Yang. Weinan Zhang, Yong Yu, and Lei Li. Mars: Markoy molecular sampling for multi-objective drug discovery. In International Conference Learning Representations, 2020.
Minkai Xu, Lantao Yu, Yang Song. Chence Shi, Stefano Ermon, and Jian Tang. Geodiff: a geometric diffusion model for molecular conformation generation. arXiv:2203.0220 2022.
Soojung Yang. Doyeong Hwang, Seul Lee, Seongok Ryu, and Sung Hwang. Hit and lead discovery with explorative RL and fragment-based molecule generation. arXiv:2110.01221 2021.
Jiaxuan You, Bowen Liu, Rex Ying, Vijay Pande, and Jure Leskovec. Graph convolutional policy network for goal-directed molecular graph generation. In Proceedings of the 32nd International Conference Neural Information Processing Systems, pp. 6412-6422, 2018.
Chengxi Zang and Fei Wang. Moflow: an invertible flow model for generating molecular graphs. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 626, 2020.
Alex Zhavoronkov, Yan Ivanenkov, Alex Aliper, Mark S Veselov, Vladimir Aladinskiy, Anas- tasiya V Aladinskaya, Victor A Terentiev, Daniil A Polykovskiy, Maksim D Kuznetsov, Arip Asadulaev, et al. Deep learning enables rapid identification of potent ddrl kinase inhibitors. Nature biotechnology, 37(9):0038 1040, 2019.
Zhenpeng Zhou, Steven Kearnes, Li Li, Richard N Zare, and Patrick Riley. Optimization of molecules via deep reinforcement learning. Scientific reports, 9(1):1-10, 2019.
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A PROOFS AND DERIVATIONS
A. EXISTENCE OF THE OOD-CONTROLLED DISTRIBUTION
is enough show that there exists a probability distribution q satisfying the following:
(G) (G) 1H,
(14)
where H (Gl ((G) } and X e [0, Let p(G)~vA - 1H. Using the fact that p(.) is probability distribution defined in G,
((G) p()))
P. PGG)dG S p. P-Vi-1 xc.
(15)
Therefore, defining the probability as = q/B shows the existence of such distribution.
A.2 DERIVING THE OOD-CONTROLLED DIFFUSION PROCESS
Using Eq. (5) model pt (y. >\Gi) to be proportional the negative exponent of the density Pe( (Gt), we can derive the following reverse-time SDE from Eq. (3):
dG, [f.(G)) (1 vA)g, V (.gg:((..). - gt Va log 1 Hr, ]. g.dw.
(16)
For sufficiently small threshold p.. obtain VG, log 1 H. O, thus the generation process simulated by the reverse-time SDE in Eq. (16) is equivalent to the generation process simulated by the following reverse- time SDE:
dG. GG. (1 vA)gī V log (G:) g.dw,
(17)
which corresponds the proposed OOD contcontroleed diffusion process in Eq. (6) of the main paper.
B ADDITIONAL REMARK ON RELATED WORK
Note that recently, Schwag al. (2022) introduced conditional coore-based model for generation of images from low-density regions, by modifying the sampling process using a discriminative model steer the generative process to the low-density region. However, it is clearly different from proposed OOD control scheme described in Section 3,1, as it 1) requires an additionally trained model sample from the low-density region, and moreover, 2) cannot control the amount of deviation of the generated samples from the in-distribution.
C EXPERIMENTAL DETAILS
C.I TOY EXPERIMENT
Following Jo et (2022), we utilize bivariate Gaussian mixture as the data distribution of the toy experiment in Section 3.1 follows:
Pdcta (x) = (x /1, Σn) + N(x 12, Σ2);
(18)
where the mean and variance are given as follows:
#1 = 0.5
-0.5
0.5 ,
0.5
1.0
0.9
Σ = Σg 0.12
0.9
1.0
We set the number of linear layers as 20 with residual paths, the hidden dimension as 512, the type of SDEs as VPSDE with 3mi 0.01 and 3maz 0.05, the number of training epochs as 5000, the batch size as 2048, and use an Adam optimizer (Kingma & Ba, 2014). We generate 2 samples in Figure with PC sampler of signal-to-noise ratio (SNR) of 0.05 and scale coefficient of 0.8.
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C.2 UMAP VISUALIZATION
To produce the UMAP visualization of the generated molecules in Figure 4, we first randomly select 5,000 molecules from the ZINC250k dataset and 3,000 molecules from REINVENT, FREED- QS, MOOD-ID, and MOOD which are generated against the target protein parp1, respectively. ChemNet (Preuer et al., 2018) activations are computed from the molecules and then together visualized by the UMAP library (McInnes & Healy, 2018).
C.3 NOVEL MOLECULE GENERATION
Measuring the novelty We measure the novelty of the generated molecules as the fraction of valid molecules with similarity less than 0.4 compared to the nearest neighbor GSNN in the training dataset, which can be formally written as follows:
1 1(sim GsNN) < 0.4),
(19)
GEM
where M is the set of valid molecules, and sim(G, G') is the pairwise Tanimoto similarity over Morgan fingerprints of radius 2 and 1024 bits.
Implementation details Following Jo et al. (2022), each molecule is preprocessed into graph of X E {0. 1 and A E (0, 2,,,,33 where N is the maximum number of atoms in molecule of the dataset, and is the number of possible atom types. The elements of A indicate the bond types (single, double, and all hydrogens are removed by the RDKit (Landrum et al., 2016) library. We utilize the valency correction proposed by Zang & Wang (2020). We use the pretrained score networks sø, and 882 from Jo et al. (2022)', which are trained on the ZINC250K (Irwin et al., 2012) dataset with the same train/test split used by Kusner et al. (2017). Following the original paper, for diffusion of node and adjacency matrices, respectively, and set the SNR and the scale coefficient as 0.2 and 0.8, respectively. As in Jo al. (2022), we quantize the entries of the adjacency matrices by mapping the values of (-oo, 0.5) to O, the values of [0.5, 1.5) to 1, the values of [1.5, 2.5) to 2, and the values of [2.5, +o0) after the sampling.
triple). All molecules are preprocessed to their kekulized form
VP and VE SDEs
C.4 PROPERTY OPTIMIZATION
Scoring function We the popular docking program QuickVina 2 (Alhossary al., 2015) to compute the docking scores and set the exhaustiveness as I, following Yang et al. (2021). Note that the docking scores are negative values. QED and SA scores are computed using the RDKit (Landrum et al., 2016) library. To compute the objective function of Eq. (13), we clip the docking score in the range [-20, 0] and compute DS and SA as follows:
DS
- 10-SA
DS
SA
(20)
20
Following Yang al. (2021), choose five proteins, parp1 (Poly [ADP-ribose] polymerase-1) 1), fa7 (Coagulation factor VII. 5htlb (5-hydroyyrrptammin receptor 1B), braf serine/threonine-pottce kinase B-raf), and jak2 (Tyrosine-protein kinase JAK2), that have highest AUROC scores when the protein-ligand binding affinities for DUD-E ligands are approximated with AutoDock Vina, as the target proteins about which the docking scores are calculated.
Scheduling the scaling coefficients Instead of manually setting the value of the scaling coefficients of the Boltzmann distribution 01,ı and a221, we automatically set the value through the time-dependent magnitude ratios Tı, and r2,,, respectively, throughout the diffusion process shown in Eq. (11). The ratios are in turn scheduled according to time as follows:
Fi = 11,0 0.1",
72, = 12,0 0.1%,
(21)
where 71,0 and r2,0 are the final values (when = 0) of rı, and r2,c respectively.
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Evaluation metrics Novel hit ratio is the fraction of unique hit molecules that have the maximum Tanimoto similarity less than 0.4 with the training molecules, which can be written as follows:
(DDS(G) > (the median DS of the known active molecules), QED > 0.5, SA(G) < 5}.
GEM
(22)
where n is the number of total generated molecules, and M is the set of generated molecules with no duplicates. Novel top 5% docking score is the average DS of the top 5% of total generated molecules with no duplicates that satisfy the following constraints: QED > 0.5, SA <,, and sim G. GsNN) < 0.4. GsNN is the nearest training molecule of the generated molecule G, and sim G G') is the pairwise Tanimoto similarity over Morgan fingerprints of radius and 1024 bits.
Implementation details The implementation details regarding the preprocessing of data, the model of GDSS, and the postprocessing procedure are the same as explained in Section C.3. We perform the grid search with the search space À E {0.01, 0.02, 0.03, 0.04, 0.05). and find À 0.04 performs reasonably well throughout the experiments. Regarding the hyperparameters of the property prediction network. we set the number of the GNN operations L as 3 with the hidden dimension of 16. The number of linear layers in MLPs and MLP, are both I, and the number of linear layers in the final MLP, is 2. We perform the grid search with the search space 11.0 E (0.3, 0.4, 0.5, 0.6, 0.7, 0.8), and set 11.0 as 0.5, 0.4, 0.6, 0.7, and 0.6 for the optimization with the target protein as parp1, fa7, b, braf, and jak2, respectively. We find that 22,0 = (i.e., O2,t 0) performs reasonably well regardless of the target.
Implementation details of the baselines We follow the corresponding original papers for most of the settings of the baselines. We describe the specifics and the differences from the original papers here. For REINVENT, we utilize the ZINC250K dataset to construct the vocabulary and train the prior". For MORLD, we set the absolute value of docking score from Quick Vina 2 as the final reward function and use benzene as the initial molecule For HierVAE, we use the ZINC250K dataset to construct the vocabulary and pretrain the model We follow the procedure utilized in Yang et al. (2021) to finetune the model for the optimization task. Specifically, we finetune the model using the DUD-E active molecules of the target protein as the training set, and the number of training epochs as 800 for 5htlb and 700 for other proteins, since the 5 training set is larger. We adopt the two- cycle active learning scheme that gathers the generated hit molecules in the first round, then utilize them as additional training molecules in the second round. Note that although the active learning scheme improves the performance of VAE, also requires twice of docking computations as the other methods. For FREED and FREED-QS, we utilize the predictive error-PER". For LIMO, we utilized the pretrained VAE model and train the property network to predict the docking score from Quick Vina 2, and generate molecules without the filtering based on the ring size for fair evaluation
Implementation details of Table 3 For the comparison with the 3D molecule generation baselines, we train GDSS and MOOD on the CrossDocked2020 (Francoeur et al., 2020) dataset with the same train/test split used in Luo et al. (2021a) and Peng et al. (2022). We utilize the molecules with less than 40 atoms the training set, which corresponds to 96.77% of the original training set. We wwwatylggloossiin--pppeee
choose glmu hit threshold as the docking score of the reference ligand contained in the test set. For the model of Luo et al. (2021a), we utilize the pretrained model without the duplication or ring filtering for fair evaluation". For Pocket2Mol, we utilize the pretrained model and generate molecules with 5,000 initial molecules, and collect the first 3,000 generated molecules without the duplication filtering for a fair evaluation
uridyltransferase) as the target protein, and set the
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Table 4: Novel molecule generation results on the QM9 dataset.
A
FCD
NSPDK MMD (x10-3)
Novelty (%)
0
3.794
0.354 2.119
44.033
0.15
6.276
70.533
C.5
COMPUTING RESOURCES
We conduct all the experiments on TITAN RTX, GeForce RTX 2080 Ti, or GeForce RTX 3090 GPUs.
D ADDITIONAL EXPERIMENTAL RESULTS
D.1 NOVEL MOLECULE GENERATION
To verify that the proposed OOD-controlled diffusion scheme can control the OOD-ness of the gener- ated samples, we additionally conduct the novel molecule generation task on the QM9 (Ramakrishnan et al., 2014) dataset. We report the FCD, NSPDK MMD, and novelty results in Table 4.
D.2 PROPERTY OPTIMIZATION
We report the property optimization results of additional baselines that not based distribution learning or a fragment vocabulary Table 5 and Table 6. GCPN (You et al., 2018) is an atom-based RL model that utilizes adversarial training. Graph GA (Jensen, 2019) is genetic algorithm-based model that utilizes predefined crossovers and mutations. MORLD (Jeon & Kim, 2020) is an RL model that uses QED and SA scores as intermediate rewards and docking scores final rewards with the MolDQN algorithm (Zhou et al., 2019). As shown in the tables, MOOD outperforms the baselines in most target proteins, and this performance gap increases with the harsher novelty condition of 0.3 as shown in Table 7 and Table 8. These results show that MOOD is indeed very effective in generating drug candidates that are both novel and high-quality and superior in de novo drug discovery tasks even to the methods that do not conduct distribution learning or utilize fragment vocabulary.
We also additionally report the novelty, diversity, uniqueness, hit ratio, and the top 5% docking score of the generated molecules in Table 9, Table 10, Table 11, Table 12, and Table 13. Novelty is the fraction of valid molecules with similarity less than 0.4 compared to the nearest neighbor in the training set, explained in Section C.3. Diversity is calculated based the pairwise similarity Morgan fingerprints of the generated molecules. Uniqueness is the fraction of the valid molecules that unique. Hit ratio (%) is the fraction of unique hit molecules. Top 5 5% docking score is the average DS of the top 5% unique molecules that satisfy the constraints QED > 0.5 and SA < 5. Note that the high novelty MORLD shown Table arose from the fact that MORLD does not utilize any training molecules nor fragment vocabulary extracted from known molecules, and LIMO also exhibits high novelty due its inceptionism- like technique applied to the learned latent space. However, the novelty values are trivial as MORLD and LIMO completely fail to generate high-quality and meaningful molecules. As one can observe in Table 1, Table 2, Table 12, and Table 13, the majority of the generated molecules of MORLD and LIMO do not satisfy the basic QED and SA constraints or do not exhibit high binding affinity. Also note that the case of HierVAE, the validity is very low and since FCD and NSPDK MMD only take valid molecules into account, the FCD and NSPDK MMD values do not contain much information.
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Table 5: Novel hit ratio (%) results. The results are the mcans and the standard deviations of runs. The best performance and comparable results (p > 0.05) are highlighted in bold.
Target protein
Method
parp1
fa7
Shilb
braf
jak2
GCPN (You et al., 2018)
0.056 (t no16)
0.444 (#: 0.553)
0.444 (t: 0.150)
0.033
(# 0.027)
0.256 (:: 0.87))
Graph GA (Jensen, 2019) MORLD (Jeon & Kim, 2020)
4.811 ( 1661)
0.422
0.198)
7,011 2.732)
3.767
1.498)
5.311 (+1.667)
0.047 (t 0.50)
0.007 (t: 0.033)
0.880 ( 0.735)
0.047
(= 0.040)
0.227
(+: 0.118
MOOD (ours)
7.017 (4: 0.479)
0.733 0.341)
18.673
0.42)
5.240
0.285)
9.200
(+: 0.524)
Table 6: Novel top 5% docking score (kcal/mol) results. The results are the means and the standard deviations of runs. The best performance and comparable results (p > 0.05) are highlighted bold.
Target protein
Method
parp1
fa7
Shtlh
braf
jak2
GCPN (You et al., 2018)
-7,464 (1 0089)
-7.024 (1 0.629)
-7.632 (1 0,059)
-7.691 0.19))
-7.533 (1 0.140)
Graph GA (Jensen, 2019)
-10,949 ( u.32)
-7.365
(#: 0.326)
-10,422 (+ 0.670)
(t: 0.341) -10.789
-10.167 ct: 0.576)
MORLD (Jeon & Kim, 2020)
-7.532 0.360)
-6.263
0.165)
-7.869
0.650)
-8.040 0.33))
-7.816 0.138)
MOOD (ours)
-10.865 (1 0.113)
-8.160 (1 0.071)
-11.145 (1 0,042)
-11.063 (11 0.04)
-10.147 (1: 0.060)
Table 7: Novel hit ratio (%) results with the similarity condition 0.3. The results are the means and the
standard deviations of 5 runs. The best performance and comparable results (p >> 0.05) are highlighted in hold.
Target protein
Method
parp1
fa7
Shtlb
braf
jak2
GCPN (You el al., 2018)
0.044 ( 0016))
0.378 (#: 0.333)
0,344 c 0.126)
0.000 (# 0.000)
0.222 (d: 0.113)
Graph GA (Jensen, 2019) MORLD (Jeon & Kim, 2020)
0 (1 0,134)
0.011
(1: 0.016)
0.644 (1: 0.40)
0.267 (:: 0.309)
0.778 (10.468)
0.040 (t 0.039)
0.007
0.033)
0.760 c:: 0.80)
0.033 0.037)
0.207
(+: 0.106)
MOOD (ours)
4.107 0.405)
0.387 0.13)
10.687
3.293
0.351)
5,525 (1: 0.578)
Table Novel top 5% docking score (kcal/mol) results with the similarity condition of 0.3. The results are the means and the standard deviations of 5 runs. The best performance and comparable results (p > 0.05) are highlighted in bold.
Target protein
Method
parp1
fi77
5htlb
braf
jak2
GCPN (You et al., 2018)
-7.347 (+: (ow)
-6,870 (t: 0.579)
-7.445 (d: (oze))
-7.589 (#: 0210:
-7.426 (#: (.141)
Graph GA (Jensen, 2019)
-7.558 0.13))
-5.423
0.164)
-7.465 (t 0:558)
-8.059 (+ 048))
-7.780 0445))
MORLD (Jeon & Kim, 2020)
-7.253 (#: 0 0.198
-6.037 (1: 031)
-7.734 (#t 0.570)
-7.572
cz 0212)
-7.560 (:: 0.187)
MOOD (ours)
-10.585 (+: 0.124)
-7.740 (t: 0.070)
-10.817 (+ n009)
-10.754
(t: 0.089)
-9,876 (:: 0.105)
Table 9: Novelty (%) results. The results are the means and the standard deviations of runs The best results are highlighted in bold. The results of GDSS and MOOD-w/o Ps are the same for the different target proteins.
Target protein
Method
parp1
Shtlb
braf
jak2
REINVENT (Olivecrona al., 2017)
9.894
2.18)
10.731
1516)
11.605
3688)
8.715 (L. 2012)
11.456 (=: 1.993)
MORLD (Jeon & Kim, 2020)
98.433 (t: 1.18%
97.967 ct: 1766:
98.787
(# 0.54)
96.993 ct 2267)
97.720 (= 0995)
HierVAE (Jin et al., 2020a)
60.453
(+17616) 24.853
15416)
48.
1988)
59.747
(+16400) 85.200 (=14.62))
FREED (Yang et al., 2021)
71.483
1.21%)
57.687
8808)
64.460
(200 65.560 (211 72.607 (= 5.170)
FREED-QS
74.640
(t 2.55))
78.
c 2132)
75.027
(= 5.394)
73.653
ct 4312)
75.907
(= 5916)
LIMO (Eckmann al., 2022)
99.356
0.247
98.589
0042)
94.267
( 1688)
98.756
ct 0220)
98.911
(= 0.185)
GDSS (Jo et al., 2022)
75,933 (1: 0.427)
MOOD-w/o Ps (ours)
79.460 (t 0.221)
MOOD-ID (ours)
72.607 3.184)
75.793
137)
70.321
1.529
70.667 (a: 1.24)
69.947 1323)
MOOD (ours)
84. 180
2.123) 83.180 (1 1519) 84.613 (1 0322) 87.413 (L 0830) 83.273 (. 1.45)
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Table 10: Diversity results. The results are the means and the standard deviations 5 runs. The best results
are highlighted in bold. The results of GDSS and MOOD-w/o Pg are the same for the different target proteins.
Target protein
Method
parp1
fa7
5ht
braf
jak2
REINVENT (Olivecrona et al., 2017)
0.827 (1: 0.007) 0.842 (1: 0.006) 0.841 (1: 0.006)
0.831 (1 0.065)
0.851 (1: 0.004)
MORLD (Jeon & Kim, 2020)
0.895 (=: 0.00) 0.893
0.896 (=: 0001) 0.893 (= 0.02)
0.895 (t: 0.01))
HierVAE (Jin et al., 2020a)
0.724 0.000 0.725 (1: 0.002
0.739 (2 0.008
0.749 (2: 0.003)
0.762 (1: 0.012)
FREED (Yang et al., 2021)
0.831 (# 0.010)
0.842 0.00)
0.831 (# 0010)
0.837 (# 0.08))
0.808 (+: 0.10))
FREED-QS
0.855 (#: 0.003)
0.855
(= 0.00)
0.850 (=: 0.002)
0.851 (#: 0.063)
0.850 (t: 0.003)
LIMO (Eckmann et al., 2022)
0.894 (= 0.002)
0.898
(1) 0.001)
0.891 (#= 0.002)
0.893
(# 0.0013
0.894 (#: 0.01)
GDSS (Jo et al., 2022)
0.887 0.094)
MOOD w/o P& (ours)
0,886 (1: 0,005)
MOOD-ID (ours)
0.884 (#: 0.001)
0.887
(# 0.000
0.878 (t: 0.01) 0.003) 0.872 (1: 0.003) 0.862 (1 0.000) 0.866 (1: 0.001)
01880 (#: 0.00)
0.875 (# 0.82)
MOOD (ours)
0.873 (1: 0.005)
0.889
Table 11: Uniqueness (%) results. The results are the means and the standard deviations of 5 runs. The best results are highlighted in hold. The results of GDSS and MOOD-w/o Pg are the same for the different target proteins.
Targel protein
Method
parpl
fa7
Shilh
braf
jak2
REINVENT (Olivecrona et al., 2017)
99.781 (= 0.365)
99.780
(:t 1211)
99.706
ct 0.661
99.663 0250)
99.714 (t: 0-407)
MORLD (Jcon& & Kim, 2020)
99.427
0.666)
99.320 0884)
99.880
0.09)
99.367
99.667
0.173)
HierYAE (Jin et al., 2020a)
4.480 [1: 0.645)
6.667 t1: 0.977)
4.707
(1: 1,221)
5.773
(2: (.21)
4.053 (1L 0.365)
FREED (Yang et al., 2021)
97.153 (L 2.886)
97.593
(1 1.87))
95.133
(1 3385)
96.760
2.00)
96.667
(1: 2.382)
FREED-QS
100.000 < 0.000) 99.980
(2: 0.000
100.000
c 0.00) 99.913
(t: (178)
99.940
0.120
LIMO (Bekmann et ul., 2022)
99 556 (1 0.228)
99.511
(1) 0.208)
92.322
(1 4,280)
99.478
(1.0.277
99.689
(1 0.02)
GDSS (Jo et al., 2022)
99.833
0.098)
MOOD-w/o Pa (ours)
99 827 (1: 0,065)
MOOD-ID (ours)
98.76 767 (1: 0.335)
99.613 1. 100)
98. 28. (t: 0.407)
97.300 (1: 0.19)
97.860 cE: 0.485)
MOOD (ours)
98.860 (#: 0.455)
99.600 (2 1388)
98.467 (# 0,322) 98.693 (s: 0.354) 95. (z 0.43)
Table 12:
Hit ratio (%) results. The results are the means and the standard deviations of 5 runs. The best results are highlighted in bold.
Target protein
Method
parp1
fa7
Shilb
braf
jak2
REINVENT (Olivecrona et al., 2017)
4.693 1.776) 1.967 (1: 0.661)
26.047
2.49)) 2.207
0,800)
5.667 (1L: 1.067)
MORLD (Jcon & Kim, 2020)
0.047 (t: 0.50)
0.007 (+: 0.013)
0.893 (=28) 0.047
(# 0040)
0.227 (+: u.118)
HierVAF (Jin al., 2020a)
1.180 (t: 0.183)
0.033 (t 0030)
0.740
(371) 0.367
0.187)
0.487 (:: 0.183)
FREED (Yang et al., 2021)
4.860 (1: 1415)
1.487 02222
14.227
(2: 5.11)
2.707
(1: 0,721)
6.067 (::: 0.790)
FREED-QS
5,960 (1 0,902)
1.687 (1 0.177)
23.140
(1: 2.42))
3,880
0.623)
7.653 (LL 1.373)
LIMO (Eckmann et 2022)
0.456 (t: (357)
0.044
(t: 0.016)
1,200
(=18))))
0.278
0.134)
0.711
(+: 0.329)
GDSS (lo et al., 2022)
2.367 (t: 0.316)
0.467 (t: 0.12)
6.267
(= 02277)
0.300
(t: 0.198)
1.367
(d: 0.258)
MOOD-w/o Pa (ours)
2,360 (t: 0.234)
0.480 (d: 0.09))
9.907
(= 0.234)
0.627 r4: 0.132)
2.780 (d: 0.280)
MOOD-ID (ours)
3.860 0.177)
0.587
15.393
0.567)
2.860
5.07.
(:: 0.437)
MOOD (ours)
7.260 (1: 0,764) 0.787
(1: 0. 128)
21.427
(1: 0.502)
5.913 (1: 0,311)
10.367
(::: 0.616)
Table 13: Top 5% docking score results. The results the means and the standard deviations of 5 runs. The best results are highlighted bold.
Target protein
Method
parpl
fa7
Shtlb
braf
jak2
REINVENT (Olivecrona et al., 2017)
-10.447 (t 0.10)
-8.510
(.111
-10.474
et 0.000
-10.363
(z 0.136)
-9.565 (t: 0.07))
MORLD (Jeon& & Kim, 2020)
-7.580 (# 0273)
-6.293
0.167)
-7.877
(663)
-8,081
(360))
-7.833
0.135)
HierVAE (Jin et al., 2020a)
-9,581 0.95)
-6.842
(. 0,200
-8.178
(1 0225)
-9.029
(ú 0.21)
-8.347
(1L 0.134)
FREED (Yang el al., 2021)
-10.607 ct: 0166)
-8.440
(= 0.65)
-10.627
ct 0283)
-10.493
(.47
.9.772
(1: 0097)
FREED-QS
-10,709 (a: 0.100)
-8.475
0.000)
-10.830
0.144)
-10.702
(á 0.074)
-9.849
0.069)
LIMO (Bekmann et al., 2022)
-8,986 cá: 0222)
-6.771
(= 0.147)
-8.447
ca 005t)
-9.048
cá: 0.519)
-8.449
(1: 0.274)
GDSS (Jo et al., 2022)
-10.095 0091
-7.921
o.06)
-9.619
-9.447
0.544)
-9.027
0071)
MOOD-w/o Ps (ours)
-10.155 c# 0.37)
-8.021
(= 0,51))
-9.949 ct n064)
-9.769
(t: 0.44)
-9,350 (z: 0.45)
MOOD-ID (ours)
-10.488 (# 0.022)
-8,081
(= 0.41)
-10.602
0.05))
-10.581
(= 0.000)
-9.695 0.054)
MOOD (ours)
-10.898 (a: 0.117)
-8.229 (=: 0,070)
-11.194 (1 0.04))
-11.135
(1: 0.037)
-10.194 (1: 0.259)
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Table 14:
Property optimization results against target protein parpl with various values The results are the means and the standard deviations of runs. The best results are highlighted in bold.
A
Novelty (%)
Novel hit ratio (%)
Novel top 5% DS (kcal/mol)
0.03
81.867 (4: 2.47))
5.944 (= 0.735)
-00.804 0.61))
0.04
84.180 (4: 2.123)
7.017 (#= 0.428)
-10.865 (e: 0.113)
0.05
85.467 (#: 0.694)
6.444 (= 0.457)
-10.803 (1: 0.086)
Table 15:
Dockstring F2 task results. The results the means and the standard deviations of runs. The best results are highlighted bold.
Method
Score
FREED (Yang al., 2021)
-3.391 0.209)
LIMO (Eckmann al., 2022)
-0.318 (#: 0.102)
MOOD (ours)
-3.920 (:: 0.021)
To see the effect of À on the property optimization task, we additionally provide the property optimization results with various values of Table 14, where 0.04 is the setting used in the main experiments. As shown in the table, novelty increases as the value of A increases as in the novel molecule generation task. However, the results of 0.03 and À 0.05 are worse than that of A = 0.04 in terms of novel hit ratio and novel top 5% DS, since molecules that deviate from the training distribution naturally tend to low-quality, and balancing the effect of the OOD control and the property gradient is important to produce novel and high-quality molecules.
We additionally report the results of the task of the Dockstring benchmark (Garefa-Ortegoe et al., 2022) in Table 15. The score of the task is calculated as follows:
DS (w.rt. target protein F2) + 10 x (1 QED).
(23)
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REINVENT
HierVAE
FREED-OS
MOOD-ID
M00D
Generated
Sim: 0.676 DS:
Simc 0.582 (SS
Sim: 0.425 OSS +1.7
Sim: 0,466 06:-90
Sim: 0.356 / DS: -8.
ZINC250K
ZIN250K Generated
Shith
0.84/D5.
Sim: 0.461/ DS: 9.4
0.596 DS:
0.532/ /S5
Sim: 0.360/ / DS:
Sim: 0.725 DS: 40.5
Sim: 0 /0///15111 11.2
Sim: 0.476 os 41.3
Sim, 0.565 DS.
Sim: 0.310 / DS: -114
ZINC250K
Generated
Jak2
Sim: o, 0.781 0.:-9.6
Sim: 0.518 DS -9.4
D6:
323 -10.5
ZINC250K
Figure 8: Generated hit molecules and the corresponding molecules from the ZINC250k dataset of the highest similarity. The similarity and docking score (kcal/mol) are provided the bottom of each generated hit.
D.3 ADDITIONAL MOLECULE SAMPLES
We additionally provide samples the generated molecules and the training molecules that are maximally similar to those molecules in Figure 8. As shown in the figure, while the molecules generated by the basclines exhibit high Tanimoto similarity, the molecules generated by MOOD do not share big substructures with the training molecules, even in the maximally similar one.
21


Reviews:
[{"review_id": "oWKyFG0R8q2", "reviewer": "Reviewer_xSWJ", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The goal of the paper is to extend molecule generation using diffusion models to include a way to control how “out-of-distribution” generated molecules should be. In order to do this, the authors propose adding a term to the reverse-diffusion score (using an SDE formulation) along with a manually tuned hyperparameter $\\lambda$ which controls “OOD-ness”. The authors demonstrate that their method is capable to generating molecules which are unique from the training set, yet still likely have realistic bioactive properties using some computed proxy metrics (i.e. docking score, drug likelihood score, and synthetic accessibility score).", "summary_of_the_review": "Overall, the paper demonstrates a novel method to control the OOD-ness of generating samples from a generative diffusion model. Their analyses demonstrate convincingly that their method can be used to generate samples that are different from the training set. They also show that within these OOD molecules, there can be found molecules which are expected to have certain bioactive properties.\n\nI find the main weaknesses to be that the paper only focuses on a single computational proxy for bioactivity (which arbitrarily combines a few metrics into a single optimization goal). Thus, the method may not be very robust: it might not work if we want to optimize for a different set of molecular properties. Additionally, there are no analyses that show how many of the generated molecules (OOD or otherwise) are reasonable. It is very possible that the vast majority of molecules generated are garbage.\n\nTogether, I think that the contribution of OOD control is interesting and this paper is a good proof of concept, despite its missing analyses that could really show its usefulness in more applications.", "strength_and_weaknesses": "Overall, I like the idea of controlling OOD-ness seems somewhat novel, and I think the authors do a good job of demonstrating that by controlling $\\lambda$, the OOD-ness can be adjusted. Their analysis of OOD-ness using FCD and MMD (with associated dimensionality-reduction plots) is convincing to me. I also think the combination of OOD-ness with conditional optimization (i.e. the “property gradient”) is a natural next step which the authors address and show results for.\nBelow are some things I believe could be stronger:\n### Property prediction is limited to a single, manually crafted objective\nIn order to show property prediction, the analysis focuses entirely on a single objective, which combines DS, QED, and SA scores into a single scalar (using the product). It is not clear why this is the chosen objective. The degree of manual tuning in this objective might suggest a lack of robustness in the results. For example, why not use an objective which is the sum of these three scores (with adjustable weightings)?\nIt would be more convincing if we could see three more distinct property models, each one trained to predict DS, QED, or SA separately. Since the authors are using classifier guidance, the score model would not need to be retrained. Showing that MOOD can then optimize for OOD molecules which show better DS, QED, or SA scores separately would greatly increase the confidence that the method is working and is not limited to a specific, manually crafted objective.\n### OOD molecules may generate large numbers of “garbage” molecules\nIn order to evaluate how well the model generates molecules which satisfy the property objective, the analysis seems to focus entirely on “novel hit ratio” and  “novel top 5% docking score”, which are defined to measure how well the “most OOD” molecules satisfy the property objective. However, these metrics are limited to comparing only the generated molecules which already have a good property score (i.e. the analysis is limited already to molecules which pass certain thresholds). Thus, it is very possible (if not likely) that many molecules generated by this method (not just OOD molecules, but also when $\\lambda$ is set to 0) are “garbage” molecules which do not actually correspond to any bioactivity.\nIt would be much more convincing that this method works, if the authors could compare these property values (i.e. DS, QED, and SA) of all generated molecules (not just those that pass DS/QED/SA thresholds) between their methods (MOOD/MOOD-ID/MOOD-w/o-P) and a couple of benchmarks.\n### Effect of $\\lambda$ on OOD-ness\nIt would be nice to also see how the magnitude of $\\lambda$ can affect OOD-ness; for example, if lambda is increased further, does it also increase OOD-ness?\n### Smaller details\n- How is the UMAP in Fig. 4 generated?\n- In Fig. 6, it is not clear what the relationship is between the ZINC250k molecules shown and the MOOD-generated molecules: are they the closest ZINC250k molecules based on MMD? Or something else?\n- It is not clear how QED and SA scores were computed\n- The property-prediction conditional score in Eq. 9 depends on $\\lambda$, but it seems (under the last section of Section 3) that the authors don’t actually use lambda in the property-prediction score model. Although this makes some empirical sense, it conflicts with the derivations in Eq. 7 – 9. It would be more clear to have Eq. 7 – 9 assume conditional independence between OOD-ness and property labels to begin with.\n- In the sentence following Eq. 13, it should explain what SA is (in structural biology, SA could also refer to solvent accessibility)", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}, {"review_id": "j4o-54rAmY", "reviewer": "Reviewer_ZWEt", "summary": "", "questions": "", "limitations": "", "rating": 1, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes MOOD (Molecular out of distribution diffusion), a method using diffusion models to generate novel molecules which differ frrom training molecules and potentially have desirable properties. The method essentially modifies the reverse-time SDE equation to reduce the coefficient of the $\\nabla \\log{p}$ (score) term and add a term involving a property predictor. Experimentally they demonstrate that MOOD produces molecules which are:\n1. Different than the training set\n2. Possess desirable properties using an oracle based on molecular docking", "summary_of_the_review": "This paper proposes a potentially interesting idea to a problem which I don't think is actually a problem; instead it is just a shortocming of several popular models in ML over the past 5 years. The derivation of the method itself is unclear, which makes the method seem not very principled (EDIT: further discussions with the authors make me think that several key equations are incorrect due to a mis-use of Bayes rule, so I lowered my score). I do not find the experimental results convincing, particularly because of the omission of a large class of important baseline methods. Together, these shortcomings imply that the paper should not be accepted.", "strength_and_weaknesses": "**Strengths**:\n\n- The core idea of using a diffusion process to generate novel molecules is interesting and could potentially be useful\n- The experimental results on 5 non-trivial oracles are interesting and encouraging. I appreciate that they didn't use logP/QED/other trivial oracles\n- Writing is very clear\n\n**Weaknesses**\n\n- _Problem is not well-motivated_: the authors state in many places that MOOD is designed to overcome the inability of existing methods to explore areas of chemical space away from the training data. While some methods do have this limitation, a huge number of methods do not, for example methods using genetic algorithms [1, 2] or graph enumeration [3]. Put simply, producing molecules which are \"different\" is **not** an open problem which would benefit from the development of new methods. My guess would be that the authors are not aware of a lot of earlier literature on this topic (most citations are ML papers from the past 5 years). I would like to see the authors correct this, and perhaps have a more nuanced discussion about the pros/cons of existing methods. Roughly, this would probably be that exploratory methods can propose new molecules but many of them are of low quality, while generative models can propose higher-quality molecules but they are generally more similar to the training data. MOOD could then be described in the context of this trade-off.\n- _Mathematical motivation for MOOD is not convincing_. My first concern is that the definition of $y_0$ used to arrive at equation 6 is unclear. The description somewhat implied that it was a binary random variable indicating whether or not a given graph $G$ is OOD, but this would imply a distribution on the set {0, 1} not $[0, 1)$. However, it is also described as a hyperparameter, which means it is _not_ a random variable and therefore writing $p(G|y_0=\\lambda)$ and $p(y_0=\\lambda|G)$ does not make sense. Equation 5 only adds to this confusion, since it is written as a distribution over $y_0$, but the \"derivation\" in appendix A.1 treats it like a distribution over $G$ (which I think is a mistake). It also seems to not be a valid probability distribution if $p(G) < p_*$, since equation 5 suggests $p(y_0)=0$ (i.e. it would not normalize to 1 and therefore is not a distribution). Overall this path to arrive at equation 6 makes very little sense to me. I think the authors would need to more clearly define the interpretation and role of $y_0$, and fix any errors in the reasoning that follow (for example if $y_0$ is a random variable then the proof in A.1 is not correct). My second concern is that construction of equation 9 is not really explained at all. My guess is that the authors intended to substitute their model for $p(G_t, y_0, y_p)$ into equation 2, but this is not correct, because it neglects the gradient $\\nabla_G\\log{Z(G)}$, i.e. the gradient of the normalizing constant in equation 8. The authors should clarify this. Finally, in equation 11, setting the coefficients $\\alpha$ to values which depend on the score seems like it would have implications for the correctness of the reverse-time SDE, but this is not discussed (I could be wrong about this though). **Overall**: the key equations of MOOD do not seem to have a principled justification.\n- _Missing important baselines_: the baseline methods used by the authors are all methods which tend not to produce OOD molecules. While the inclusion of these baselines is good, the authors should of course include baselines which do not suffer from these problems (see discussion above). The open-source methods from [4] could be a good starting point, for example Graph GA. These methods will almost certainly explore as well as MOOD or better, and could plausibly also produce higher-scoring molecules in section 4.2\n- _Issues with metrics in section 4.2_: the novel hit ratio and novel top 5% docking score are both normalized by the number of unique (hit) molecules, which can be problematic (assuming I have understood them correctly; if not then the authors should explain their metrics more clearly). For example, out of 3000 molecules, method A produces just 2 unique molecules (one novel hit and one poor molecule), it's novel hit ratio would be 100%, while method B producing 500 novel hits, 500 similar hits, and 2000 poor molecules would have a novel hit ratio of 50%. I think method B would be superior in this case, while the author's metrics would favour method A. Novel top 5% docking score suffers from similar problems. I think the authors should either report standard metrics, or continue to sample from all methods until a certain number of unique hit molecules are produced, which would fix the normalization problem.\n- _Lack of experiments on standard benchmarks_: while I support the authors creation of a new, reasonable molecular optimization benchmark, the problem with just evaluating MOOD on a novel task is that the general difficulty and idiosyncrocies of this task are not understood, so it is unclear how much of the method's success is \"general\" and how much is due to being particularly well-suited for these specific tasks. I think that evaluating MOOD on at least one standard benchmark would be useful. One option would be to use the benchmark from PMO [4], which includes a variety of semi-toy functions such as GuacaMol. These are not as realistic as docking, but have also been tried with many more baselines, which would help contextualize the performance of MOOD. A second option using docking would be dockstring [5] which contains several standardized docking benchmarks.\n\n[1] Nigam, AkshatKumar, et al. \"Beyond generative models: superfast traversal, optimization, novelty, exploration and discovery (STONED) algorithm for molecules using SELFIES.\" Chemical science 12.20 (2021): 7079-7090.\n\n[2] Jensen, Jan H. \"A graph-based genetic algorithm and generative model/Monte Carlo tree search for the exploration of chemical space.\" Chemical science 10.12 (2019): 3567-3572.\n\n[3] Ruddigkeit, Lars, et al. \"Enumeration of 166 billion organic small molecules in the chemical universe database GDB-17.\" Journal of chemical information and modeling 52.11 (2012): 2864-2875.\n\n[4] Gao, Wenhao, et al. \"Sample efficiency matters: a benchmark for practical molecular optimization.\" arXiv preprint arXiv:2206.12411 (2022).\n\n[5] García-Ortegón, Miguel, et al. \"DOCKSTRING: easy molecular docking yields better benchmarks for ligand design.\" Journal of chemical information and modeling 62.15 (2022): 3486-3502.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "1: The main claims of the paper are incorrect or not at all supported by theory or empirical results.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "9o9JWfAIcg", "reviewer": "Reviewer_3YM5", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The present paper is concerned about a generative model of molecules. The authors consider that the existing generative models are limited in that i) the generated molecules are similar to those in the training dataset, while what we want are very novel molecules, and ii) the target properties used in common benchmark tasks are not very helpful for drug discovery and existing methods are not likely to fully optimize more realistic multi-objective optimization tasks due to their limited exploration capabilities. Thus, the authors propose a molecular out-of-distribution diffusion (MOOD) framework, where the score-based model is guided by the property prediction network to generate out-of-distribution molecules with desirable properties. \n\nIn particular, the authors define the ODD-ness of a graph in Eq. (5) and use it to guide the generative process towards increased ODD-ness. The effectiveness of the ODD controller is showcased in Figure 2. In addition, the authors utilize property prediction networks to guide the generative process towards maximizing the properties. These two guidances are valanced by the magnitudes of the two related score functions.\n\nIn the experiments, the authors first confirm that their ODD controller can actually control the ODD-ness of the generated molecules. The authors then compare the proposed method with baseline methods in terms of novel hit ratio, which asks the method not only to optimize the objective function but also to be dissimilar to the molecules in the training dataset. The results show that the proposed method achieves the highest novel hit ratios. The authors also provide ablation studies.", "summary_of_the_review": "I consider this paper is a border-line paper. While the method proposed is well designed to achieve the research objective, I am not fully convinced of the need of OOD-ness. It could be a mean to further optimize the objective function, but I am still not sure whether the OOD-ness itself is to be pursued or not. In addition, the property prediction or simulation-based property calculation could be inaccurate for OOD molecules, which de-motivate me to pursue OOD-ness. Therefore, to better assess the usefulness of this paper, I would like to request the authors to clarify i) whether the OOD-ness itself is pursued or it is just a mean to optimize the score, and ii) risks of pursuing OOD molecules and ways to avoid them. I would also appreciate it if the authors could point out my misunderstandings if any.", "strength_and_weaknesses": "## Strengths\n- The proposed method is a solid improvement over existing score-based graph generative models, whose effectiveness has been shown empirically.\n- The evaluation metrics in the experiments are well designed to be aligned to the research objective, to find out-of-distribution molecules.\n- Reproducibility is maintained as the supplementary material contains the code.\n\n## Weaknesses\nI am still not sure whether the generated molecules have to be out-of-distribution. A molecule similar to those in the dataset will be acceptable if its properties are sufficiently optimized; in other words, if we have two molecules that have similar properties but one of them is close to the training dataset while the other is far from the training dataset, then is the out-of-distribution molecule preferred? If not, then the novelty is not an end but a mean, and it is not natural to incorporate the novelty into the evaluation metric.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works.", "empirical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}, {"review_id": "3b75w3Zgcr", "reviewer": "Reviewer_gMda", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "Summary of the paper\nThe paper extends the score-based generative models by Song & Ermon (2019) to control the OOD level of generated molecules. To constrain the generation process such that it targets generating only OOD examples having desirable properties, they utilize the gradient of a property prediction network to guide the sampling process.\n\nThe authors demonstrated that the given approach outperformed the existing works on generating new drugs both in terms of novelty and having higher binding affinity confirmed by docking methods.\n\n", "summary_of_the_review": "This is a minor extension of existing score-based generative models. Comparison with VAE models by Payes Das et al. (https://www.nature.com/articles/s41551-021-00689-x) on conditional generation and adjust the VAE to control the novelty in the latent space could be a potential simple baseline to compare to.", "strength_and_weaknesses": "Strengths\nThe paper was well-written, it addresses a practical issue of AI-based approaches. \n\nWeaknesses\n\nRegarding the proposal of a controlled parameter for OOD sampling from a score-based model,  it is worth comparing the given approach to the VAE, where OOD sampling in VAE can be controlled by the deviation of the sampled latent variable to the predicted Gaussian distribution given by the encoders. I see a comparison to LIMO (Eckmann et al., 2022) but in the experiments with LIMO for novel drug generation, did you sample the latent variable using a constant factor deviating from the predicted standard deviation to control the novelty? \n\n\nDrugs (Antimicrobial peptides) generation conditioned on a few desirable properties is not a new idea, please refer to Payes Das et al. (https://www.nature.com/articles/s41551-021-00689-x). The difference between the prior art is that it trains a conditional VAE to control the desirable property constraint while the (MOOD) framework is based on a score-based model and utilizes the gradient of a property prediction network to guide the sampling process to domains that are highly likely to satisfy the given constraints. I see a comparison to LIMO (Eckmann et al., 2022)  but the given method was not trained to generate molecules that have the constraint on desirable properties. This is not a fair comparison.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject