Unified Guidance for Geometry-Conditioned Molecular Generation
Authors: Sirine Ayadi
Leon Hetzel
Johanna Sommer
Fabian J Theis
Stephan Günnemann
Venue: NeurIPS 2024 poster (2024)
Keywords: generative models
conditional diffusion
Primary area: machine_learning_for_physical_sciences

Abstract: Effectively designing molecular geometries is essential to advancing pharmaceutical innovations, a domain, which has experienced great attention through the success of generative models and, in particular, diffusion models. However, current molecular diffusion models are tailored towards a specific downstream task and lack adaptability. We introduce UniGuide, a framework for controlled geometric guidance of unconditional diffusion models that allows flexible conditioning during inference without the requirement of extra training or networks. We show how applications such as structure-based, fragment-based, and ligand-based drug design are formulated in the UniGuide framework and demonstrate on-par or superior performance compared to specialised models. Offering a more versatile approach, UniGuide has the potential to streamline the development of molecular generative models, allowing them to be readily used in diverse application scenarios.

Unified Guidance for Geometry-Conditioned Molecular Generation
Sirine Ay2
Leon Hetzel*1:22
Johanna Sommer" 1,2
Fabian T223
Stephan Günnemann' 1.2
School of Computation, Information and Technology, Technical University of Munich 2 Munich Data Science Institute. Technical University of Munich Center for Computation Health, Helmholtz Munich {si ayaddy 1.hetzel, jm. sommer, f f.theis, wug.uuenmmnn @tum. de
Abstract
Effectively designing molecular geometries essential to advancing pharmaceu- tical innovations, domain, which has experienced great attention through the success of generative models and, in particular, diffusion models. However, current molecular diffusion models are tailored towards specific downstream task and lack adaptability. We introduce UniGuide, framework for controlled geometric guidance unconditional diffusion models that allows flexible conditioning during inference without the requirement of extra training or networks. We show how applications such as structure- based, fragment- based, and ligand- drug design are formulated in the UniGuide framework and demonstrate on-par superior performance compared to specialised models. Offering a more versatile approach, UniGuide has the potential to streamline the development of molecular generative models, allowing them to be readily used in diverse application scenarios.
Introduction
Diffusion models have emerged as an important class of generative models in various domains, including computer vision [1], signal processing [2], computational chemistry, and drug discovery [3-8]. By gradually adding noise to data samples and learning the reverse process of removing noise, diffusion models effectively transform noisy samples into structured data [9, 10]. In the context of drug discovery, it is essential to effectively address downstream tasks, which often pose specific geometric conditions. Examples of this include (i) Structure-based drug design (SBDD) that aims to create small ligands that fit given receptor binding sites [11], (ii) Fragment-based drug design (FBDD) that designs molecules by elaborating known scaffolds [12. 13], or (iii) Ligand- based drug design (LBDD) which generates molecules that fit certain shape [14]. Recent works address these tasks by either incorporating specialised models or focusing on conditions that directly resemble molecular structures. In both cases, this narrow focus restricts their adaptability to new slightly altered settings.
We address the challenge of adaptability by introducing UniGuide, a method that unifies guidance for ceometry-conditionn molecular generation, see Fig. 1. The key element for achieving this unification is the condition map, which transforms complex geometric conditions to match the diffusion model's
Equal contribution
Project Page: www.cs.cit.tmm www.sss....ttutceooommmmmm wtt.ttmm.do//dm//mmiiiiiide
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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(1) Langet recopcor
(R) rocoptor hagmont
shape
UniGuida
Nov dewiias
Aawee Valaen
Unitauiie
Lnitaride
UniCaaie
Condition Map
2
Delea Condtton
Any
Self Guided Modd
UniGuide
UniGuide handles diverse conditioning modalities for guidance, including: (i) target receptor for SBDD, (ii) additional molecular fragments for FBDD, or (iii) a predefined 3D shape for LBDD. It combines a source condition 8 E S and the unconditional model eæ t) within its condition map to enable self-guidance. The flexible formulation of our approach can be generalised new geometric tasks, for example, conditioning on atomic densities.
Figure 1:
configuration space, thereby enabling self-guidance without the need for external models. Like other guidance-based approaches, UniGuide does not constrain the generality of the underlying model. Moreover, our method is the most versatile, extending beyond guiding molecular structures to leveraging complex geometric conditions such as volumes, surfaces, and densities, thereby enabling the unified tackling of diverse drug discovery tasks. For complex conditions specifically, previous works primarily rely on conditional diffusion models for effective condition encoding [12-14]. With our method, we are able to tackle the same tasks, while overcoming major drawbacks: UniGuide climinates the need for additional training and, more importantly, avoids constraining the model to specific tasks.
We demonstrate the wide applicability of UniGuide by tackling a variety of cromeety-coosttained drug discovery tasks. With performance either on par with or superior to tailored models, we conclude that UniGuide offers advantages beyond its unification. Firstly, while the novelty of conditional models often stems from the condition incorporation, our method redirects focus to advancing unconditional generation, which directly benefits multiple applications. Furthermore, this separation of model training and conditioning allows us to tackle tasks with minimal data, a common scenario in the biological domain.
In summary, our contributions are as follows:
We present UniGuide: A unified guidance method for generating geomeety--onddioned molecular structures, requiring neither additional training nor external networks used guide the generation.
We demonstrate UniGuide's wide applicability by tackling various conditioning scenarios in structure-based, fragment-basee based, and bgsend-based drug design.
We show UniGuide's favourable performance over task-specific baselines, highlighting the practical relevance of our approach.
2 Related work
Diffusion models and controllable generation Diffusion models [9, 10] are generative models achieving state-of-the-art performance across various domains, including the generation of images [1, 9]. text [15], or point clouds [16]. Conditional diffusion models [17-21] are based the same principle but incorporate a particular condition in their training. allowing for the controlled generation. Alternatively, classifier guidance [22, 23] relies on external models for controllable generation. Prior works in this context primarily focused on global properties [22, 24], lacking the capacity to condition on the geometric conditions central to work. For instance, Bao et al. [24] demonstrate control over molecule generation based on desired quantum properties.
De novo molecule generation Research on de novo molecule generation focused extensively on generating molecules using their chemical graph representations [7, 25-34]. However, these methods are limited in modelling the molecules' conformation information and are, therefore, not ideally suited for several discoviry settings, such as target-aware drug design. Recently, attention has shifted towards generating molecules in 3D space, utilising variational autoencoders [35], autoregressive models [36-38], How-based models [39, 40), and diffusion-based approaches [20, 41-47)

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Conditional generation of molecules Downstream applications of molecular generation can be categorised by their condition modality. the case of SBDD [38, 48, 49], Schneuing et al. [11] and Guan et al. [50], for example, introduce models that simultaneously operate on protein pockets and ligands. In the conditional case, the pocket context is fixed throughout the generation. Moreover, FBDD imposes (multiple) scaffolds as a constraint [11, 12, 51-53J. Igashov et al. [13] expand given scaffolds by generating the molecule around the fixed scaffolds. design with pose estimation, as discussed in [54], further generate the rotation of the given scaffolds. SBDD and FBDD rely on the availability of high-quality data of protein pockets, which often scarce. For this reason, LBDD aims generate molecules that match the same 3D volume of reference ligands that are known to bind to the target of interest [55, 56]. Chen et al. [14] specifically train a shape encoder to capture the molecular shape of reference ligand and use the resulting embedding to train a conditional diffusion model.
related task of FBDD, linker
Controlling the generation of diffusion models
Diffusion Models [9, 57] learn Markov Chain that involves forward process to perturb data from a distribution g(z) and learn to reverse the process to generate new samples from tractable prior, for example, a normal distribution. Given data point sampled from the true underlying distribution, Zdata (z), the forward process (ze (1) gradually adds Gaussian noise:
g(Ze /2 = (2: V1 1,,
where {3, (0, 1)}- defines a variance schedule. Deñnnng the forward process this way, one can readily sample from q(z Z:aa):
Ze Vāizaa +
e~ c0,,1,
with 11 3g and ãe IT Q; Since the time-reverse process ( (2) depends on Zalata
which is not available at generation time, it approximated by modelling po 2:)::
po(2,-1 2.) (2:-1 no (zr, o1))
(3)
where the mean png is parameterised by noise-predicting neural network eg in the form of:
B. E
(z
at Z:
VI az
The model eg is trained to optimise the variational lower bound through the simplified training objective:
Linin = - Ea(2,,
Self-guiding diffusion models condition can be expressed
Using Bayes' rule, the conditional probability po |c) given a
po (Ze c) x po (ze) po(c| 2t).
This allows us to decompose the score function as follows:
V log (z c) = Vz, log (z.). + S SV.. (o zz),
(7)
where the second term is used for guiding the unconditional generation, with S 0 controlling the guidance strength. Using that Vz, log Po po(2.) -(1 - -0 t) [22], function from Eq. (7) and identify the modified noise predictor ég:
rewrite the score
Vz, (z c)
VI a² co(Ze, t) v S V (c 2;)
(8)
=iēo =iēo (z)
The modified mean function pa then follows from the modified version of Eq. (4), enabling us to sample from pa(z.-1 kr, C) N (z 1, (,,)),,))
3r
ju (z,, t, c) = vat
Zi
Eo(Ze, t, c))== po( t) + V(t) log zz)
(9)
v1
3

---

2 3.S balances the conditional update. Eq. (9) requires sampling from log pc 24) which we do not have access. Assuming the condition lies in the same space as we can follow Kollovieh et al. [58] and approximate log po (c 2z) as multivariate Gaussian distribution:
where A(t) (ax)
pa(cl (e (z(::)),1)
(10)
where fo (z. t) approximates the clean data point, enabling to estimate the condition in data space. Using Eq. (2), readily predict the clean data point given the noisy sample Z, via
So(zr, 1) Z1 vI āi Eo (z
20
(11)
With this, the guiding term becomes a direct differentiation of the squared error with respect to the noisy sample ze:
po(cc - - fo cl1
(12)
By directly leveraging the prediction of the unconditional model cØ. Eq. (12) establishes our self- guiding conditioning, thereby defining the self self-guided noise predictor éØ:
és(Z,, (, = E0(2,, 1)+ VI a.S
20
c
(13)
4 UniGuide
To enable the application of unconditional molecular diffusion models to geometric downstream tasks in drug discovery, we aim to develop unified guidance framework, UniGuide, see Fig. Importantly, we seek to enable guidance from arbitrary geometric conditions S, where S denotes a general space of source conditions. However, the source conditions 8 cannot be directly used for the loss computation in Eq. (12) when they do not match the configuration space Z.
To address this challenge, we introduce condition maps C, which bridge the gap between arbitrary source conditions 8 and target conditions с suitable for guidance. In Sec. 4.1, we start with its general formulation and continue to derive a condition map Cz for the special case where S Z. This will be useful when discussing the application of UniGuide to various drug discovery tasks in Sec. 4.2. We also demonstrate how derive a task ssecifpec condition map Cav for ligand-based drug design.
Notation In 3D space, the configuration of molecules, including proteins, can be represented by a set of tuples = (ar; [. E Z, where æ; E TR3 and h, E R refer to coordinates and features of node 2, (æ;, h2), respectively. The space of configurations is denoted by 2 and includes confiuurations of varying size N. We distinguish between different configuration entities via superscripts, i.e. refer to molecules M and proteins P through Z and z², respectively. The collection coordinates x = {oI...... AN E Nx3 E X' defines the conformation of a molecule M protein P. We represent arbitrary geometric conditions with the variable E S, and conditions that can be used for guidance with the variables c E Z.
4.1 Unified self-guidance from geometric conditions s E S
The concept of condition map C is essential E S in a unified fashion, where S represents a space of general geometric objects such as structures, densities, surfaces. These geometric objects do not necessarily match the configuration space Z, ie. * Z, preventing the computation of the guiding score function from Eq. (12). We overcome this challenge by defining as a transformation that maps suitable target condition Z, which is then utilised for self-guidance.
method, enabling guidance from conditions
In the most general case, C' takes the form of
C:Sx Z 2
(14)
8
x Z +
where the source condition together with configuration are mapped to target condition c 2. Including the condition map C in the guidance, we obtain our guidance signal:

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V log (c|c z,) 2 nn
V ||00 C(s, 20]112=
(0s,20))12 - - C(zn,
(15)
where 2n = (zz. t) is the estimate of given the unconditional model eø(z;, t) obtained according to Eq. (11) and
Css, 2n) is the target condition produced by the condition map. In this formulation, e can also be understood as guidance target of the unconditional model.
It is important to highlight that Eq. (15) should not destroy the underlying properties of the uncon- ditional generative process. In particular, if the unconditional model 6a is equivariant to a set of transformations G. e.g. rotations and translations, retain equivariance also in the guidance signal. Hence, the self-guided model ég should satisfy
common in the molecular domain, want
Eo (G(() 1, c) (,,
(16)
for all transformations G which Eg is equivariant.
Theorem 4.1. Consider a function C: S G in the first argument and equivariant in the second argument, then the gradient Vz||v|12 of the vector z C(s, z) is equivariant to transformations of
Z. C(, z) is invariant to rigid transformations
Proof. We prove Theorem 4.1 App. B.
Using Theorem 4.1, we can guarantee equivariant guidance signals if the condition maps C(s, z) are invariant and equivariant under rigid transformations concerning the source condition a and configuration respectively.
Guidance in the special case o = In the case where the source condition s directly defines subset of < N nodes of the configuration, i.c. = Z, we can fully specify the condition map. This is feasible because the condition map no longer needs to bridge different spaces; it only needs to ensure equivariance, as the loss computation between s and the configuration is already possible. To distinguish this special case from the general setting, we denote s ž gmx and refer the defined subset within the configuration Zn by 2n²".
In order to satisfy the requirements on C(ă 2n¹) as stated by Theorem 4.1, we align ā with 2n by using the Kabsch algorithm [59, 60]. Denoting the resulting transformation with Tzg. we get an -n-quuivariant condition map:
Cz: mmx(3+d) x pmx(3+d) + pmx((+d)
(17)
2
Tep
Taken together, we can compute the guidance signal based on the following loss L:
1 C(2 2) = 1|a - T
(18)
We emphasise that although the loss [(2 2) is computed on the subset A, the gradient, as presented in Eq. (15), is still computed with respect the full configuration 2,-
In summary, our method requires only an unconditionally trained model eg and a suitable condition map C. eliminating the need for additional networks training. Together, this facilitates unified self-guidance from arbitrary geometric sources. Importantly, the separation model training and conditioning enables to tackle tasks with minimal data, which is crucial in practical scenarios. In the following section, we discuss the wide applicability UniGuide by illustrating its application to multiple drug discovery tasks.
4.2 UniGuide for drug discovery
Having introduced both the guidance framework and the condition map, will continue discuss how to tackle a set of drug discovery tasks within the UniGuide framework. We start with its application ligand-based drug design (LBDD), which aims to generate ligand that satisfies predefined molecular shape.
5

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Ligand-based drug design LBDD aims to generate novel ligands with similar 3D shape as reference ligand M,r. In this setting, one operates on the molecule level only since the protein information assumed be unknown. However, to still generate active ligands that bind to a protein pocket, one leverages the 3D shape information of a reference molecule. Specifically, the goal is to modify the generative process ég to generate ligand Zo with similar 3D shape but different molecular structure than Mrer. With Sec. 4.1 introducing all required concepts, can readily formulate a surface condition map Cav suitable to tackle the task of LBDD, see Fig. 2:
V
yj
%/a(i.
xt.)
To represent Mae'' 3D shape, we identify our source condition with set of K' points y sampled uniformly from the reference ligand's 's surface 0V, E x = S. As no features are guided, we formulate Cav with respect to the conformation space Nx3,
Cx,
Figure 2: Surface condition map Cav: For each atom co- ordinate Zs. the closest sur- face points Y) are computed. The target condition Cx.i is the projection along the mean of neighbours y, to the inside of the volume by a margin a, where | 2.112.
Cav :R Xx3
x R Nx3 Nx3
(19)
y X0 Cx
where Xo denotes the conformation of the clean data point estimation 2n as computed by Eq (11). To satisfy Theorem 4.1, Cav first aligns y with Ne by rotation Rx, E 3x33 resulting from the ICP algorithm [61]. For every atom coordinate σ; Cav subsequently computes the mean T. over i;'s 's k closest surface points:
y: Σ
EEERsh R2 with No. arg
min (C
Σ jEr
|| Rx - 2:ll2
(20)
JENa:
Finally, the individual components cx of the target condition compute as follows:
y: y 2.) if é; outside V
Cx D: á (ū. - x.) if d; inside V Ad<a otherwise.
(21)
i;;;
where d denotes the distance to the surface, d = 1 22/12, and the required distance to the surface. Note that the target condition Cx represents a valid conformation inside the surface ØV, and that Cav effectively bridges spaces from S to X. Consequently, when using Cav, the guidance signal is derived from Eq. (15) with the loss function L(2o,y). The full algorithm for guidance using Cav is presented in App. D.1.
structure-based drug design The goal of SBDD is to design a ligand that binds to a target protein operates both the molecule and protein level. Technically,
pocket In this setting,
are interested in generating a ligand zi conditioned on the protein configuration z". With the unconditional diffusion model co (z(z, t), 2, (z.M. z?²), approximating the joint distribution of prontdn pairs p( z. one can readily see that the source condition directly corresponds to the configuration of the protein pocket. Hence, we can use Cz from Sec. 4.1 and identify 2 with
zP. The guidance signal then follows from the loss L(2 xP) with c. = Cz(Z², 2, as defined in Eq. (18). We describe the sampling algorithm for the SBDD task in App. E.
Tragment-baser drug design FBDD aims to design a ligand by optimising a molecule around fragments JF that bind weakly to receptor. Similarly to SBDD, operates on both the molecule and protein level. Technically, we are interested in generating a ligand 2 conditioned on both the protein and the fragment configuration, z and v respectively. Considering the same kind of unconditional model co (2z,2 t) as in SBDD, we can use Czz from Sec. 4.1. Only now, we identify with both zº and a and write A with A = P U F. Using Eq. (18), the guidance signal directly follows from L(2 z PUF) with c = Cz P PUF 2 Pu.F The sampling algorithm is similar to the one described in App. E.
Several tasks exist within the FBDD setting [62-65]. Examples are scaffold hopping [64], where the core structure of 2
M has to be generated, but functional groups that interact with the receptor are

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Table Ligand-Bass -asse Drug Design. Results taken from Chen al. [14] are indicated with (*). We
highlight the best conditioning approach for the ShapeMol backbone in bold and underline the best approach across all methods.
only shape
Method
Simy (1)
max Sim, (1)
Simo ())
mix Sima: (3)
Ratio (t)
Diversity (
Nor-
VS" [14]
0.729 1: 0.04
0.807
0.04
0.226 1 0.04
0.241
0.09
3.226
0.759 0.02
diffusire
SQUID" [55] (A= 0.3)
0.717 + 0.08
0,904
4 0.07
0,349 = 0.09
0.549 = 0.24
2.054
0.687 1: 0.07
based
SQUID [55] (A- 1.0)
0.670 1: 0.07
0.842
1 0.06
0.235
1 0.05
0.271
1: 0.09
2.851
0.744 1. 0.05
ShapeMol [14]
0.677 + 0.04
0.797
0.04
0.239
0.05
0.240 = 0.07
2.834
0.714 0.05
ShapeMol-g [14]
0.744 +: 0:03
0.849
+ 0.08
0,242
= 0.04
0.245 = 0.05
3.074
0.708 1: 0.05
Diffusion
UniGuide (ShapeMol
0.726 +
0.827 0:00
0.248
0.05
0.239
0.651 0.05
based
UniGuide (ShapeMol)
0.760 + 0,85
0.887
0.06
0.240
+ 0.04
0.237
IM66
3.167
0.705 + 0.04
UniGuide (EDM)
0.749 + 0.04
0.860
0.212 0.04
0.206
3.536
0.736 0.04
fixed, or linker design [65], where the connection between separated fragments has to be optimised through the generative process, see Fig. Note that these tasks differ primarily in their application and can be treated identically from a technical perspective within UniGuide. In addition, one can also consider variations where the protein information z" is discarded. This usually aligns with switching to an unconditional model that solely models the distribution over molecules. We present results for this configuration in Sec. 5.3.
Furthermore, we would like to highlight that it is possible to combine guidance strategies within UniGuide. For example, one could incorporate version of the surface condition map Cov for FBDD to provide an additional geometric guidance signal for the atoms not included in F.
Limitations Drug discovery also involves tasks beyond purely geometric conditions, encompassing global graph properties [24]. These are excluded from the UniGuide framework. Additionally, UniGuide requires the unconditional model to be trained on matching configuration space. We discuss the broader impact of our work in App. A.
Results
In this section, we compare UniGuide to state-of-the-an models across various drug discovery tasks. To highlight the wide range of tasks to which unconditional models can be adapted through UniGuide, we conduct experiments on ligand-based (Sec. 5.1), structure- based (Sec. 5.2) and fragment- based (Sec. 5.3) drug design. We demonstrate that UniGuide performs competitively even surpasses specialised baseline models, underscoring its practical relevance and transferability to diverse drug discovery scenarios.
5.1 Ligand-based drug design
Dataset Following Chen et al. [14], we employ the MOSES dataset for the ligand- based drug design task [66]. We evaluate on test set consisting of 1000 reference ligands, from which the 3D shape conditions are extracted. For every shape condition Mies, 50 samples are generated. We refer to App. D. for further details the evaluation setup.
Baselines For the LBDD task, we compare UniGuide to ShapeMol, conditional diffusion model that is trained by conditioning learned latent embeddings of the molecular surfaces [14]. Chen et al. [14] also propose a correction technique that adjusts the atom positions based on their distance to the reference ligand's nodes, which is refered to as ShapeMol+g. Additionally, we include as baselines Virtual Screening (VS) [14], a shape-based virtual screening tool, and SQUID [55], a variational autoencoder that decodes molecules by sequentially attaching fragments with fixed bond lengths and angles. For this task, we evaluate UniGuide equipped with the surface condition map Cav from Eq. (21)) in conjunction with two unconditionally trained diffusion models, ShapeMol [U] and EDM [14, 20] as well as the conditional model ShapeMol [14]. The "only shape" column in Tab. indicates whether method uses solely the reference ligand's shape or also incorporates its atom positions.
We compare UniGuide with an alternative guidance approach adapted from Guan et al. [67] in App. D.4 and refer App. C and App. D.3 for further information on the unconditional models and the guidance parameters, respectively, In addition, inspired by the performance of UniGuide on the
7

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Table 2: Structure-Bastt Drug Design. Quantitative comparison of generated ligands for target pockets from the CroksDocked and Binding MOAD test sets. Results taken from the respective works indicated with (*). We highlight the best conditioning approach for the DiffSBDD backbone in bold and underline the best approach over all methods.
Method
Vina Score (U)
Vina Min (U)
Vina Dock (L)
QED (t)
SA (1)
Test Set
6.362 : 3.14
6.707 + 2.50
7.450 + 2.33
0.48
0.73
Noo-
Dift.
3D-SBDD" [38]
-5.754 :: 3.25
66180 + 2.42
6.746 +: 4.02
0,51
0.63
CrossDacked
Pocker2Mol* [48]
-5.139 +: 3.17
-6.415 2.93
-7.152 + 4,90
0.56
0.74
DecompDifl (No Drift) [67]
-4.750 +:
6.170
Dillusson
TargetDiff' [50]
-5.466
-6.643 4.94
+ -7.802
0.48
0.58
DifSSBDD-ond [11]
33.684
-4.670
6.06
6.941 4:
0.47
0.58
DiftSBDD [11]
-4.097 + 11.3
-.300 + 5.00
-7.889
+ 2.61
0.57
0.64
UniGuide
5,.00
8.39
6.610
4.20
7.921
+ 2.43
0.57
0.64
Diltusion- based
Test Set
-6.748 + 2.77
-7.663
2.53
8.297 +: 2.03
0.60
0.64
Binding MOAD
DinSSBD-ccond [11]
4,466 2.63
6.309 +: 2.52
7.482 :: 1.84
0.43
0.56
DiffSBDD [11]
4.744
66.86
+: -7.767
0.55
0.62
UniGuide
5.074 : 6.75
6.622
2.57
7,911 4: 1.97
0,56
0.61
LBDD task, we further motivate its applicability for the generation of molecules given atom densities, see App. G.
Evaluation
The goal of LBDD is dis- cover novel molecules that fit within a given
Generated Reference Genented Referonce
Reference
Gemerated
3D shape. This can quantified by a high 3D shape similarity and low graph similarity compared to the reference ligand, as illus- trated in Fig. 3 as well as App. D.2. We highlight this trade-off by reporting the ratio of these similarities in Tab. 1 as Sims/ /Simg,
0
Shape Similiarity
which constitutes the most important met- ric for this task. We follow Chen et al. [14]
and further evaluate the mean and maximum shape similarities Simg and max Sims, re- spectively, per reference ligand, measured via the volume overlap between the aligned molecules. Additionally, we report the graph similarity Simg defined as the Tanimoto sim- ilarity between the generated and reference ligand, and the graph similarity max Simg of the generated molecule with the maximum shape similarity. Further metrics concerning the quality of the generated ligands are provided in App. D.2.
Tanimoto: 0.200
Shape Similarity 0.01
Figure 3: Examples of the two shape-conditiones lig- ands generated by UniGuide. The goal is to have low molecular graph similarity and high shape similarity.
Both in terms of shape similarity and graph similarity, guiding the generation of EDM with UniGuide outperforms other task-specific conditioning mechanisms and even the Virtual Screening baseline. Emphasised by the Ratio metric across all evaluated methods, UniGuide demonstrates that is able generate diverse molecules with very similar shapes compared to the reference ligand. Remarkably, UniGuide achieves higher shape similarity than ShapeMol+g. even though the conditional model explicitly guided towards the position of the reference ligand through the position correction technique. UniGuide, on the other hand, does not require information about the reference's 's atom positions at all to generate novel, high-quality ligands. This highlights how UniGuide and the design of condition maps enables unconditional models like EDM, that have not been tailored or trained for the LBDD task, to achieve state-of-hh--an performance on new tasks.
5.2 Structure-based drug design
Datasets Following Schneuing et al. [1]], we evaluate UniGuide on two protein-ligand datasets: the CrossDocked dataset [68] and the Binding MOAD dataset [69]. For the CrossDocked dataset, we follow the preprocessing as described by [38] and conduct the evaluation 100 test protein pockets.

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Table Linker Design. Results taken from Igashov al. [13] are indicated with (*). We underline the best method overall.
Method
QED (t)
SA(()
Rings (1)
Valid
Unique (1)
Filters (1)
Recovery
Non-
Delinker+ ConIVAE+ MMMF [53]*
0.64 + 0.16
311==06h
0.21 :: 0:042
96.3
44.2
84.8
80.2
diffusion
301 Inker (53j"
0.65 + 0.16
3.14 0.66
0.24 + 0.4
71.5
29.2
X3.7
93.5
based
3DLinker (given anchors) (52]*
0.65
0.23
99.3
29.0
84.2
94.0
DiflLinker [13]"
0.65 0.15
3.19 = 0.27
0.32 0:04
90.5
51.4
87.9
70.7
based
Diflusion
inker (given anchors) [13j"
0.65 + 0.15
3.24
0.81
0.36 4: 0.59
94,8
50.9
84.7
77.5
UniGuide (EDM)
0.64 +: 0.16
3.63 1.08
0.49 0.2
89.1
72.1
87.9
58.8
The Binding MOAD dataset is preprocessed as discussed in Schneuing et al. [11], resulting in 130 test proteins. Per target pocket, 100 ligands are generated. We evaluate the generation of ligands on models that are trained on the full-atom context of the pockets in Tab. 2 and results of models trained on the Ca representation of the pockets are provided in App. E.5.
Baselines We compare UniGuide to two autoregressive models designed for the SBDD task: 3D-SBDD [38] and Pocket2Mol [48]. We further include TargetDiff [50] and DecompDiff [67], conditional diffusion models for SBDD that fix the protein pocket context during every step of the diffusion process. We exclude approaches with explicit drift terms like Guan et al. [67] and Huang et al. [70] from the comparison, as UniGuide's SBDD condition map does not include drift terms currently, but can be readily extended to do so. Schneuing et al. [11] present two techniques for controlled structure-basse
generation: (i) DiffSBDD-cond, a conditional diffusion model similar to [50] and (ii) DifSSBDD an inpainting-inspired technique that modifies the generative process of an unconditional diffusion model that jointly generates protein-ligany pairs. Across datasets, both UniGuide and DiftSBDD control the same unconditional ligand-proteid diffusion model. We provide more information and further evaluation regarding this base model in App. E.2 and App. E.3 and investigate the influence of the guidance scale S well as the resampling trick [7 11. a technique that modifies the generative process to better harmonise the generated ligand with the controlled pockets, in App. E.4 and App. E.5.
Evaluation As the task of SBDD is to generate ligands that bind well to a given protein pocket, we assess generated ligands based on affinity-reatted metrics (Vina Score, Vina Min and Vina Dock), which estimate the binding affinity between the generated ligands and given test receptor [72]. Additionally, we measure the quality of the generated ligands using two chemical properties: the drug-likenest (QED) and the synthetic accessibility (SA) [66, 73].
Tab. 2 demonstrates that, without addi- tional training or external networks, UniGu- ide performs competitively with even the highly specialised conditional models like TargetDiff and DecompDiff. Our results indicate that not fully converging to the target protein pocket due to soft guidance, compared to, for example, DifISBDD's innspie technique, is not lim- itation in practice. Rather, it suggests that utilising self-guidance in combination with a suitable condition map generates well- harmonised ligand-protein pairs. This is also reflected in the properties of the gen- erated ligands, where UniGuide achieves good
VINA Dock: -8A
VINA Dack -1433
VINA Dack: -1233
0.354
QED: SA: 0.750
OED:
SA: 0.330
Figure 4: Qualitative example of a test protein pocket (6c0b) from the Binding MOAD dataset. We show the reference ligand (grey) and samples generated by UniGuide (blue).
(QED) and synthetic accessibility (SA) scores. We provide additional qualitative examples for the SBDD task in Fig. 4, which showcase that UniGuide not only generates drug-like ligands but even able to improve over the VINA Dock metric of the reference ligand.
5.3 Fragment-based drug design
Datasets & Baselines In the following, we investigate linker design, subfield of fragment-based drug design. We follow Igashov et al. [13] and decompose ligands from the ZINC dataset [74] with the MMPA algorithm [75]. Note that the ZINC dataset does not contain pocket information, and the evaluated approaches operate solely at the molecular level. We compare UniGuide to DiffL innk
[13], diffusion- based conditional model that fixes fragments in space. Additionally, we evaluate

---

the variational autoencoder- based methods DeLinker [53] and 3DLinker [52], adapted as described in Igashov et al. [13]. We provide more information on the experimental setup as well as the unconditionally trained EDM model in App. F.1 and App. C.
Evaluation Following Igashov al. [13]. we evaluate the generated linkers and lig-
Reference
Fixed Fragments
ands with respect their properties (SA,
Linkinng
QED, Number of Rings and 2D Filters). We
additionally measure (i) the uniqueness of the generated samples, (ii) the recovery of
the reference ligands, and (iii) the validity, which combines the chemical validity and the successful linking of the fragments.
VINA Dock: -00.8
VINA Dock: -11.0
Growing
Using UniGuide to control the EDM gener- ation enables the successful combination of the condition fragments and the generation of diverse linkers. Even compared to task- specific models, UniGuide is able to per- form competitively across different metries. Importantly, UniGuide enables the same un-
VINA Dock: -11.2
VINA Dock: -10.2
Scaffolding
conditional model (EDM) tackle both the
linker design task as presented in Tab. 3 as
well as the LBDD task as presented in Tab. without additional training. Note that, while DiffLinker is specifically designed to gener- ate linkers, UniGuide readily generalises to other tasks within the FBDD setting, such as fragment growing and scaffolding, see Fig. 5, Additionally, UniGuide is agnostic to the fragmentation procedure used to obtain the condition scaffolds, meaning that UniGuide will generalise to unseen fragments long as the underlying molecule fits within the training distribution. In App. F.2, demonstrate how the same unconditional model can be adapted for these tasks. Our quantitative evaluation highlights the benefits achieved through the unification of controlled generation provided by UniGuide.
VINA Dock: -11.2
VINA Dock: -9.9
Figure 5: For various pocket-conditioned FBDD tasks, show reference ligands (grey), desired fragments (magenta), and ligands generated by UniGuide (blue).
Conclusion
In this work, we present UniGuide, a unified way of controlling the generation of molecular diffusion models towards geometric constraints. UniGuide generalises to multitude of drug discovery tasks without the need for conditioning networks or specialised training protocols, enabling UniGuide to find applicability also in scenarios where little data is available. By demonstrating that specialisation not a necessity and that a more flexible, unified method outperforms specialised approaches across tasks and datasets, we open up new avenues for streamlined and flexible generative models with wide-ranging applications.
Acknowledgements SA, LH, and JS are thankful for valuable feedback from Marcel Kollovich, Leo Schwinn, and Alessandro Palma from the DAML group and Theis Lab. SA is supported by the DAAD programme Konrad Zuse Schools of Excellence Artificial Intelligence, sponsored by the Federal Ministry of Education and Research. LH is supported by the Helmholtz Association under the joint research school "Munich School for Data Science MUDS". FJT acknowledges support from the Helmholtz Association's 's Initiative and Networking Fund through Helmholtz AI (ZT-I-PF-5-01) FJT further acknowledger support by the BMBF (O1IS) I 8053A). In addition, FJT consults for Immunai Inc., Singularity Bio B.V., CytoReason Ltd, and Omniscope Ltd and has ownership interest in Dermagnostix GmbH and Cellarity.
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[84] William E. Lorensen and Harvey E. Cline. Marching cubes: A high resolution 3D surface construction algorithm. In Proceedings of the 14th annual conference on Computer graphics and interactive techniques, SIGGRAPH '87, pages 163-169, New York, NY, USA, August 1987. Association for Computing Machinery, ISBN 978-0-89991-227-3 URL https: /dl. acm. org/ 110.:///0...111110/0010......111
doi: 10. 10.1145/3700..3742
16

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A Impact Statement
Our research holds the promise of significant contributions to the advancement drug discovery, possibly assisting in the discovery of novel pharmaceutical compounds. Nevertheless, because of its applications in drug discovery. this strategy is not without its hazards. The ability to produce various molecules with desired properties may not only serve the purpose of beneficial drug development but may also unintentionally result in the creation of dangerous substances or compounds with unexpected effects. These concerns underline the critical need for careful handling when working with the structures this method can generate.
B Proof of Theorem 4.1
First, recall Theorem 4.1 that we provide in Sec. 4:
Theorem Consider function : + 2. (f, is invariant to rigid transformations G in the first argument and equivariant in the second argument, then the gradient Vz|[oo12 of the vector ((s, z) is equivariant to transformations of
Proof. We start the proof by showing that ||o||2 is invariant to transformations of both and 8.
1. ||z Css, 2) 222 is invariant to transformations in
Gz C(s, Gz)ll2
|Gz GC(ss l1
[C equivariant in =]
G(z C(s 2))
(22)
C(s, 2)
[G is a rigid transformation]
2. ||z C(s, | is invariant to transformations follows immediately:
| - DCCGGs = |z C(s, 2)
[C is invariant in s]
(23)
In second step, we make use of the fact that for a group of transformations G, it holds that if ((:-)) G-invariant function, v_L(-, x)) is G-equivariant [76]. From the invariance of ||v||2, it follows
immediately that Vzllz C(ss, z) || is equivariant to transformations of z.
C Unconditional Equivariant Diffusion Model
UniGuide guides an unconditional diffusion model given an arbitrary condition and a natural choice for model operating only the molecule level is the EDM model proposed in Hoogeboom et al. [20].
We adapt this model for two tasks presented in this work, namely the LBDD task discussed in Sec. 5. and the Linker Design task as presented Sec. 5.3. For these tasks, we train an unconditional EDM model both on the MOSES dataset [66] in the configuration
described in Chen et al. [14] and on the ZINC dataset [74] as described in Igashov et al. [13]. For both trainings, we employ the hyperparameter configuration for the GEOM dataset described in Hoogeboom et al. [20]. We run multi-GPU trainings on 4 NVIDIA A 100 GPUs until convergence, however, a single NVIDIA A100 GPU is sufficient for this training and will only increase the training time. For inference, employ the Resampling trick as discussed in Lugmayr et al. [71] with 10 resampling steps and T 100 timesteps. EDM is available under the MIT License.
D Ligand-based drug design
D.I Implementation details
We train two unconditional diffusion models, ShapeMol [U] and EDM, to generate 3D molecules on the MOSES dataset [66], licensed under the MIT License, for which we generate 3D conformers with RDKit [73], available under the BSD 3-Clause License. We use 1, 593, 653 training samples
17

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and randomly select 1000 samples for validation. The model architecture of ShapeMol[U] is an unconditional version of the ShapeMol model proposed in Chen al. [14]. and trained with 1000 diffusion steps. ShapeMol [U] is trained with a batch size of 32 on two NVIDIA A100 GPUs for 500 epochs. Unlike ShapeMol, we do not concatenate the molecular surface embedding of the ligands to the features. For the shape-conditioned generation with position correction (ShapeMol+g), we follow the scheme proposed in Chen et al. [14]. It provides further guidance to the conditional generation by sampling 20 query points from Gaussian distribution centred around every alom in the reference ligand. The position correction adjusts the coordinates of the predicted atom positions during every generation step by pushing the coordinates close to the query points as follows:
i = (1- +o
z/n,if
Σ (E
((8.2)/n > 7,
(24)
where d( z) is the Euclidean distance, n(ē Q) is the set of nearest neighbors of t in Q and Y > O is a distance threshold. We follow the implementation of Chen et al. [2] for the position correction method by setting y 0.2 and only guiding during the first 700 denoising steps.
For the shape-conditionel generation with UniGuide, we extract the mesh of the condition ligand using the Open Drug Discovery Toolkit [77], which is available under the BSD 3-Clause revised License. The query points we use for guidance are 512 points sampled uniformly on the mesh surface. For the evaluation, we measure the shape similarity Simg as the volume overlap between the aligned generated ligand and the condition ligand. For the alignment, we utilise the ShaFP tool [78].
We provide a detailed description of the LBDD sampling algorithm in Algorithm 1.
Sampling algorithm to generate a ligand that is conditioned on a reference ligand Mier's surface, using an unconditional model eg (,, 1)) modelling the distribution over molecules. The points y E Kx are sampled uniformly from the surface of Mier, enclosing the volume V.
Algorithm 1:
Require: y, az desired margin surface, k: number of nearest neighbours Zr ~ (O, for t T to 1 do
(Sample from normal prior)
x, h, = Z4
*n x x-- -
(Compute the conformation &o of the clean approximation 2n)
Joc
For every atom 2; in &o do:
EyeN,, y
(Compute the mean of k nearest neighbors of é; in y
Compute (cx); based on Eq. (21)
(Compute component-wis condition map)
L L(X0, Gx)
= Vx
(Compute gradient of guidance loss) (Update the mean function)
11: us (z( -((1)-0 .g
2r-1 1 ~ N N(1,, o.
end for
return Zo
D.2 Additional results
For completeness, we report additional quantitative evaluation of the generated ligands' properties in Tab. 4. We also provide further qualitative results of the generated ligands for the LBDD task in Fig. 6. UniGuide generates ligands with better shape similarity to the reference ligands compared to the conditional model ShapeMol with the position correction technique.
Table 4: Additional ligand property results for the methods discussed in Sec. 5. and standard deviation and highlight the best result in bold.
We report mean
method
Connect. (1)
Unique (t)
QED
SA (1)
LogP (1)
Lipinski (t)
ShapeMol ShapeMol+g
98.8%
99.9%
0.753
0.640 1: 0.104
2.001 1: 1.360
4.979 1 0.156
97.0%
99.8%
0.751
0,630 + 0.110
1.908 + 1.508
4.874 + 0.170
UniGuide+ ShapeMol(U]
98.0%
100%
0.736
0.625 = 0.103
1.828
+ 1.463
4.974 + 08186
UniGuide (ShapeMol)
99.0%
100 100%
0.750
0.641
0.107
2.002
+ 1.374
4.982
= 0.152
UniGuide+ EDM
99.8%
99.99%
0.742
0.636 1: 0.088
1.833 1 1.221
4.994
1: 0.082
18

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Figure 6: Examples of the ligands generated by ShapeMol, Pos-Correct and UniGuide. Pos-Correct the position correction technique proposed by Chen al. [14]. Both Pos-Correct and UniGuide combined with the unconditionally trained model ShapeMol [U]. We plot the reference ligand as well as the generated ligands with their shapes.
Table Comparison of UniGuide with validity guidance for shape-based generation. We highlight the ratio metric as the most critical indicator, reflecting the balance between shape similarity and graph dissimilarity.
Simg (?)
maxSimg (?)
Simg (4)
maxSimg (1)
Ratio (?)
Connect, (t)
Unique (f)
Diversity (f)
QHD (f)
Validiry Guidance
0.59
0.76
0.20
0.20
2.96
97%
100%
0.76
0.69
UniCluide (EDM)
0.74
0.86
0.21
0.20
3.53
9996
99%
0.73
0.74
D.3 Guidance parameters
For the LBDD task, the guidance strength S is weighted by exponentially decreasing function 8. For the guided generation using the unconditional ShapeMol [U] model under the UniGuide framework, we define scale scheduler that increases with an exponent of 1.01 and weight it with you and guide from the diffusion step 1000 to the diffusion step 200. For the guided generation using the EDM model, we use a linear scale function that increases from to 15. The guidance is applied from the diffusion step 920 to the last timestep 1.
Joi
D.4 Comparison of UniGuide with alternative loss formulation
adapt the validity guidance loss from Guan et al. [50] to LBDD setting. The proposed loss grounded in the smooth distance function S(z) from Sverrisson al. [79]. which computes as:
S(x) a log Σ exp(- |0, -1011/1)1/1))
This function provides alternative approach to shape-based generation by deriving appropriate loss function Σ, S(x), rather than modifying the condition map as proposed by UniGuide. Here, S(z) implicitly defines surface through S(x) ? and points inside satisfy S(æ,) 7.
19

---

On a technical level, the gradient for validity guidance computes as follows:
N
Vx, S(rr) = Vo, -o- log Σ
exp( ( 1 10:l1=11/////)) 11112/0))
exp(...
Vx, 1/: 31:12
Σ Eexp(...)
N willa: 9:
Vv. E = Ewi
This gradient formulation is quite similar (up the weighting) UniGuide's special case S = 2, as it computes an Le loss on a given conformation ((3i)), see Eq. (18), meaning that does not generalise arbitrary geometric conditions.
We emphasise that UniGuide is more broadly applicable because it separates surface computation from gradient computation, offering two key benefits. First, since the condition map does not require differentiability, there is greater ficxibility in computing surface points. Second, the precise geometric intuition behind the condition map makes it easier adapt new scenarios, as demonstrated by application to generating density- -uiide molecules.
For the empirical comparison, selected the hyperparameters and in the surface loss computation to achieve high DICE score between the implicitly defined surface and the meshes UniGuide utilises for LBDD (a 1, 2, DICE > 0.8). Our surface calculations use the Open Drug Discovery Toolkit (ODDT), which assigns specific radii to individual atom types and employs the marching cubes algorithm to generate meshes [80].
We performed several runs around the above-specified hyperparameter configuration. The runs per- formed similarly, and we report the best result in Tab. 5. Although validity guidance for LBDD yields low graph similarity, the shape similarity remains suboptimal compared to UniGuide. Additionally, we frequently encounter numerical instability when computing the guidance term, an issue not present with UniGuide's 's formulation of LBDD. One possible explanation for this numerical instability is that the surface is defined implicitly, unlike UniGuide where it is explicitly defined. The explicit definition UniGuide allows for relating the gradient updates directly to the surface, as shown in Eq. (21).
E Structure-based drug design
Algorithm 2: Sampling algorithm to generate ligand conditioned on protein pocket iP using the
unconditional joint model co (Zz, t), where z, = [z;M 2 that models the distribution P(z z z²). The guidance signal is controlled via the guidance strength S. Note that samples from the generative process po (2:- (2x) are assumed to CoM-free.
Require: 2P S
~ N0, I)
[ (Sample from normal prior)
for 1 = To do
of n
1
o (zt: 1)/
(Compute the clean data of the pocket)
L = L(1 2p)
= (Vx, C
Vx L, Vn.C)
(Compute gradient and substract the CoM] (Update the mean of the pocket)
μ. H (Z,,t) X(t) .g
2-11 ~ N(p, I)
end for
return z (2)) 2g
M D
E.1 SBDD sampling algorithm
We provide the algorithm for inference in the SBDD task scenario in Algorithm 2.
20

---

E.2 Ligand-protedd generative joint model
SBDD aims to generate a ligand given a protein pocket: Pa(z zleu, t). We adopt DiffSBDD []]], an unconditional joint diffusion model that approximates the joint distribution p MMM Lata of generating ligand-protein pairs, where the noise predictor ca(2, z?" t) is parametrised by EGNN. Di is available under the MIT License. To process ligand and pocket nodes with a single GNN, atom types and residue types are embedded jointly. Atom and residue features are then decoded separately using atom decoder and residue decoder to E (z:M) ze: .1) and og (xM x2. ()) [1]].
For the unconditional sampling with the joint model, the number of ligand and pocket nodes is sampled from the joint node distribution p p(N-M, _N measured across training set of (M, P) technique or with UniGuide
pairs. During the modified generative process with the appainting-inspiine the number of pocket nodes is set be equal to the number of nodes in Pies, while the size of the ligand is generated from a conditional distribution P(NM N?). Since this sampling procedure leads to ligands that much smaller compared to the reference ligands found in the test set, the mean size of sampled ligands is increased by 10 for Binding MOAD and 5 for CrossDocked during ligand generation [1 1]. We utilize the unconditional base models from Schneuing al. [11], which are trained on either the C. or full-atom context from the Binding MOAD or CrossDocked datasets. However, retrain the DifTSBDD model specifically
the full-atom context of the CrossDockedd data, as we were unable to reproduce the reported results in this configuration from Schneuing et al. [1]]. We find that contrary what is reported in Schneuing et al. [11]. the model converges early and does not need a full 1000 epochs to fully train. We employ this checkpoint to evaluate both the DiffSBD inpainting insppired approach as well UniGuide. We train the model on four NVIDIA A100 GPU with a batch size of 2. 8 training epochs take approximately 24 hours.
Table 6: Hyperparameters of ligand and proteins graphs in joint models
CROSSDOCKED
BINDING MOAD
JOINT C. MODEL
JOINT FULL-
JOINT Co. MODEL
JOINT FULL-
ATOM MODEL
ATOM MODEL
EDGES (LIGAND-LIGANN)
FULLY CONNECTED
FULLY CONNECTED
FULLY CONNECTED
FULLY CONNECTED
EDGES (LIGAND--OCKKTT)
<56 Á
< Á
<8 Á
<7 Á
EDGES (POCKET-POCKET)
<5 Á
< Á
<8
<
Proteins consist of amino acids, where every amino acid is set of amino (N H). carboxyl (CO), a-carbon atom and a side chain (R) that is specific to every amino acid type [81]. The C. Co-representation of protein pocket is residue-level graph, in which the node features of the protein are represented as one-hot encodings of the amino acid type. The full-atom representation of the receptor is an atom-level graph and represents the full context of the protein pocket. Details on processed graphs of the join model p(z zz) are provided in Tab. 6. We refer the reader to Schneuing et al. [11] for more information on the hyperparameters of the joint model.
Representing ligands and proteins as graphs
Table 7: Quantitative evaluation of samples generated by the unconditional joint models [11] trained on Crossdocked (C.D.) and Binding MOAD (B.M). We report the mean over all generated ligands.
DATASET
R
T
QED (1)
SA (1)
LIPINSKI (f)
DIVERSITY (f)
CONNECTIVITY (1)
VALIITY (t)
CCD.
1
500
0.535
0.660
4.741
0.772
0.893
0.986
C.D. (C.)
10:
50
0.578
0.752
4.836
0.774
0,994
0.986
B.M. (Ca)
1
500
0.471
0.608
4.783
0.824
0.839
0.985
B.M. (Ca)
10
50
0.544
0.665
4.883
0.823
0.961
0.992
E.3 Further Comparison to DifTSBDD
In addition to Tab. 2, we follow the experimental setup as utilised Schneuing et al. [11] to compare UniGuideto DifiSBDD, which uses the same base model, in particular. In Tab. 8, we further investigate the advantages of using self-guidance combinations with UniGuide over both the conditional DifISBDD model (DiffSBDD-cond) as well as the iapainting-inspire technique
21

---

Table 8: Quantitative comparison of generated ligands for target pockets from the CrossDocked and Binding MOAD test sets. Results taken from Schneuing et al. [11] are indicated with (*). We report mean and standard deviation and highlight the best diffusion- -based approach in bold.
Vina
Vina Top 10% (1)
(E)
(1)
Lipinski (1)
Diversity (1) RMSD ())
Test Sct
-68865 + 2.35
0,476 0.20
0,728
0.14
4,340
1,14
3D-SBDD" [38]
-5,888 191
+: 2.34
0.675
4.787
0.742
Pockot2Mol" [48]
-7,058 + 2:80
-8.712 = 3.18
0.512
0.16
0.752
= 0.12
4,936
= 0.27
0.735
0.15
Graph-BP" [49]
-4.719 4.03
-7.165 + 1.40
0.502 0.12
0.307
4.883
0.844
TargeDDiff [50]
-7.318 2.47
-9.669 + 2,55
0,483
+ 0.20
0.584
0.13
4.594
0.83
0.718
0.09
0.000
0.00
DinSBDD cond
66.500 2.26
99.120 1 2.16
0.469
0.578
0.13
4.562
0.89
0,728
0.07
0.000
0.00
DHISBDD
-7.216 2:54
-9,490
2: 2.00
0.571
0.19
0.639
0.14
4,808
0.50
0.707
0.09
0.045
0.01
UniGuide
-7.320 2:27
-9.514
= 2.01
0,571 0.19
0.638
0.14
4,822
0,47
0.705
0.08
0,047
0.01
MOAD
Test Set
-8.331 2.05
0,602 0.15
0.636
4.838
0.37
Graph-BP [49]
4.843 + 2.24
-6.629 0.95
0,512 + 0.11
0,310 0.09
4.945
0.27
0.826 0.01
0.000 0.00
DinSBDD-coad
-7.172 1.85
-9.174
2.13
4.526
0.000
DiffSBDD
-7.263 + 4.19
-9.776 = 2.25
0,546 + 0.21
0.618
0.12
4.777 = 0.54
0.740
0.05
53 31
UniGuide
-7.661 2.99
-9.864
2.13
0.556
0.605
4.799
0.723
55 +
(DiffSBDD.. UniGuide reliably achieves superior VINA Dock scores compared to both DifSBBD models and performs competitively with the conditional TargetDiff model. In App. E.4 and App. E.5, we expand on this experimental comparison with further analysis of the effects of Resampling as well as the guidance strength.
E.4 Resampling
Inpainting is introduced for diffusion models to condition outputs with fixed parts [71] and can be applied for structure-based molecular tasks. Given a model that generates (z, 2 pairs at denoising step f, the protein pocket P' is replaced with the noised representation of protein context zi" This noised representation can be obtained through the forward process of diffusion models as specified in Eq. (2). However, the direct application of this method leads to locally harmonised samples that struggle to incorporate the global context [71]. In order to effectively harmonise the generated information during the entire generative process, Lugmayr et al. [71] propose technique they call "Resampling". This modifies the reverse Markov chain by moving back and forth in the diffusion process enable the model to better incorporate the replaced components.
Schneuing et al. [11] propose to use the same resampling technique to harmonise the replaced protein context with the ligand, since the replaced receptor is sampled independently of the ligand. During resampling, each latent representation is repeatedly diffused back and forth before advancing to the next time step. We found that resampling further improves the general performance of the unconditional generation, and thus improves the guided generation as well. We report results for this in App. E.5, where evaluate how the unconditional generation of the joint model is improved across different metrics with added resampling steps. We follow Schneuing et al. [1 [] in using the setting of R = 10 resampling steps and T = 50 timesteps. While DifISBDD resamples the ligand and the noised target protein pocket, we resample the guided protein pocket and ligand with UniGuide. In general, the concept of resampling can be applied to harmonise the configuration 2, with the condition c.
E.5 Guidance parameters
The guidance scale S controls the strength of the guiding signal, see Eq. (7) and it is weighted by w(()= = (()) during the generation. We use constant scale S for structure-based drug design experiments and evaluate for several guidance scale values in Tab. and Tab. 10 for models trained on the Binding MOAD dataset with C. and full-atom representation respectively. The quantitative evaluation on the CrossDocked data shown under Tab. 11 and Tab. 12 with additional metrics reported in Tab. 7. For the generation with the -a-models, we generate 100 samples for every test pocket with a batch size 50. The full generation takes approximately hours for Binding MOAD and 6 hours for CrossDocked. For the DifISBDD model trained on the Binding MOAD fullatom pocket data, we use a batch size of 15 for the generation. We use a batch size of to sample with the DiffSBDD model trained on DrokeDocked (fullatom).
vor
22

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Table 9: Results for the Binding MOAD test set with the unconditional DiffSBDD base model trained on the C. representation of the pockets combined with UniGuide and the seainninn-inspiiee technique DiffSBDD [11]. We provide results for varying the guidance scales S during our controlled generation. We also report results for the DiftSBDD-cond (C,) model trained on the C. pockets.
METIODD
8
8/T
VISA (1)
VINA Tor 10% (L)
QED
SA (7)
L (1)
DIVERSITY (7)
RMSD (3)
DDrSBDD COND (C.)
8.291
DD
1/500
5,362
8,179
0:541 0.11
1/500
-8.177
UNIGIDDE
3.0
1/500
0.543
0.
UNIGUDE
3.0
1/500
305
0.542
0.11
UNIGUDE
4.0
1/500
-6.567
-5.293
0.544
0.11
0.058
UNIGUIEE
6.0
1/500
-6.568
-5.284
0.542
0.11
UNIGUIDE
7.0
1/500
-6.575
-8.296
0.544
0.11
0.735
DurSBDD
10/50
-5.596
3.30
5.962 1.37
0.547 = 0.20
0,578 =: 0.20
4.754
0.50
0.709 a: 0.05
0.007 1: 0.01
UNIGUIDE
1.0
10/50
-5.845
-5.972
1.36
0.547 = 0.19
0.578
0.13
4.756
0.53
0.709 d: 0.05
0.216 0.21
UNIGUIDE
2.0
10/50
6.355 4:
-9.018
1.40
0.547 = 0.19
0.577
0.13
4.756
0.52
0.707 1 0.04
0.279 1: 0.03
UNIGUIDE
10050
11.05011
0.551
0:575
UNIGUIDE
10/50
-7.016
-9.023
0:578
UNIGUIDE
6.0
10/50
-7,853
-9.067
0.579
4.761
7.3 0.04
UNIGUIDE
7.0
10/50
-7,076
-9.038
0.579
0.14
0.50
0.331
For all tables, we conduct the experiments both with and without resampling. The VINA Dock score is measured with QuickVina2 [72], available under the Apache License, and the chemical properties (QED, SA, Lipinski) are measured with RDKit. We note that in all ablation tables measure the VINA Dock score on the processed molecules, following Schneuing et al. [11], while the VINA Dock score in Tab. 2 is measured following Guan al. [67]. Both the VINA Dock
and chemical properties improve with additional resampling steps (R = 10, = 50) for both datasets. Additionally, increasing the guidance scale improves the RMSD with respect the target protein, and results in generating ligands with an improved binding affinity (lower VINA).
E.6 Additional Results for SBDD
Supplementary to Tab. 2 we provide additional metrics for the evaluation of the generated ligands in Tab. 14: the validity as measured by RDKit [73] and the connectivity, representing the percentage of valid molecules without any disconnected fragments. Additionally, we report the uniqueness and novelty of the valid connected ligands.
E.7 Runtime Comparison
In Tab. 13, provide comparison of the different controlled generation mechanisms regarding their runtime. While UniGuide has a higher runtime compared to other conditioning mechanisms, as it has to compute gradients through the diffusion model at inference time, it stays comparable to other mechanisms such as inpainting.
Table 10: Results for the Binding MOAD test set with the unconditional DiftSBDD base model
trained on the full-atom context of the pockets combined with UniGuide and the impainting-nnspie technique DiffSBDD [11]. We provide results for varying the guidance scales S during our controlled generation. We also report results for the conditional diffusion model DiffSBDD-cond.
METHOD
R/T
VINa (1)
VINA TOP 10% (1)
QBD (1)
SA(t)
LIPINSKI(T)
DIVERSITY (?) RMSD
DEFSBDD COND
-7.172 1 1.88
-9.174 2.13
0.430 0.20
0.564 0.12
4,526 1 0.80
0.711 0.088
0.0.100
DEYSBDD
1/500
-6.540 = 2.00
-8.427 = 1.59
0.413
0.20
0.531 # 0.31
4,611 = 0.77
0.745 = 0.03
55
UNIGUUDE
6.0
1/500
-6.096 = 1.78
.8.561 = 1.58
0.407
0.19
0.527 a 0.31
4.587 0.78
0.240 = 0.04
55
UNIGRIDE
7.0
1/500
-6.683 + 1.91
.8,575
1.52
0.406
0.19
0.524
0.11
4.570
0.880
0.738 + 0.04
51
UNIGUIDE
8.0
1/500
66.82
1 1.77
8.355
1.52
0.407
0.19
0.526
0.11
4,591 0.78
0,740 1 0.04
55 31
UNIGUIDE
-6.689
1.74
-8.541
1.50
0.524
4.589
0.04
DEYSBDD
10/50
-7.263 + 4.19
.9.776 = 2:25
0.546 0.21
0.618
0.32
4,37T + 0.54
0.740 = 0.05
$3 31
UNIGUIDE
5.0
10/50
-7.470 1 2.97
-9.621
1.84
0,563
0.20
0.605 0.12
4,307 1 0.50
0.723 1 0.05
51
UNIGUIE
0.05
UNIGUIDE
9.793
2.06
0.339
0.605
0.05
UNIGUIDE
8.0
10/50
-7.635
2.71
-9,821
3.07
0.558
0.685
0.12
0.50
0.730
0.05
UNIGUIDE
9.0
10/50
-7.661
2.99
-9.864
2.13
0.556
0.20
0.605 1: 0.12
4.799 0.50
0.723 1 0.05
23

---

Table 11:
Evaluation of the samples generated for the CrossDocked test set using the joint ligand-
protein diffusion model trained on the Ca pocket representation for varying guidance scales S. The base model is combined either with the inpaitning inspiired technique (DiffSBDD) or UniGuide. We
further report the evaluation of the molecules generated by the conditional model DiffSBDD-cond that is trained the C. pocket representation.
METHOD
R/T
VINa (2)
ViNa Tor 10% ())
QLD
(A)
LIPISKKI (t)
DiveRSITY (1)
RMSD (.)
DumSBDD-COND (Ca)
-6.770 2.73
0.475 0.22
0.612
4.536
0.06
0.000 0.00
Dur5BDD
1/500
-6.485
2.50
-8.472
0.510 0.21
0.619
0.12
4.640
0.73
0.735 0.06
0.053
UNICIUIEE
1/500
2.64
-8.527
0.518
0:623
4.649 0.73
0.739
0,085 0:001
UNIGUIEE
1/500
-6.
2.57
.8556
0.519
4.657
0.070 0.00
UNIQUIDE
1/500
6.577
2.72
8.563
0.518
4.659 0.71
0.741
0,059
UNIGLMRR
1/500
UNICUIDE
4,683
DIDSBDD
10r50
-7 07.000022
3.39
-9.057 =: 1.79
0.559 + 0.21
0.730
0.12
4,729 =: 0.66
0.720 = 0.07
0.052 + 0.01
UNICUUIO
1.0
10/50
-6.3 9.9999
3.35
-9.069 1.79
0.563 + 0.21
0.734 + 0.12
+.743=00.57
0.721 =: 0.06
0.711 0:1.1
UNIGUIDE
2.0
10/50
7.011
3.20
9.115
1.79
0.562 1 0:0.1
0.233 1 0.112
4.735
1 1.600
0.721 1 0.07
0,188 1 0.00
UNIGUIDE
3.0
10r50
-7.081
2:955
-9. 99.100
1.83
0.560 1 0.
0.252
0:11
4.742
0.557
0.725 a 0.007
0.127 1:0.1
UNIGUIDS
4.0
10550
-1 086
3.27
-9. -9.125
1
0.561
0:0 19
0.251
2 0.110
4.729:2000
0.719 2:
0.102 0:0
UNIGUID
5.0
10550
-1 -1.117+ +.7.8
-9.127 1.78
0.561
+
0.731
+012
4.738=
0.722 0.007
0.090 + +000
UNIGUIDE
6.0
10/50
-7.113 3.00
-9.133
1.30
0.556
+ 0.30
0.731
0.12
4.734
0.66
0.720 0.332
0.077 + 0.001
F Fragment-based drug design
F1 Linker Design
For the experimental evaluation of the linker design task, we follow Igashov et al. [13], employ the ZINC dataset [74] and preprocess it following Igashov et al. [13]. That is, 3D conformers are generated from the SMILES strings present in the dataset with RDKit [73]. We fragment the dataset ligands using an MMPA-based algorithm [75, 73J, generating multiple fragment conditions per molecule. We train an unconditional EDM model for this task as specified in App. C. For the evaluation metrics, we follow Igashov al. [13]. Note that the synthetic accessibility score computation (SA) in Tab. 3 differs from the remaining experimental evaluations. While Igashov et al. [13] report the SA score S5A directly, Schneuing al. [1 report the SA score as (10- sga)/9.
For the task of linker design, we adjust the condition map as discussed in Sec. 4.2 slightly to include anchor information, similar in spirit to the DiffLinker model incorporating anchor information [13]. That is, additionally to guiding parts of the molecule to the desired fragment configuration, we additionally define cuboid's surface that is defined from the specified anchor atoms. We can then utilise this surface condition Cav to guide the linker atoms in accordance with Eq. (21). Additionally, we can expand this surface based the linker size ensure chemical validity of the generated linker. This condition map highlights the flexibility of UniGuide condition maps in various tasks, especially through the combination of two definitions of the condition map. For the experimental evaluation, we sample the size of the linker nodes uniformly in accordance with Igashov et al. [13] and compare to the DiffLinker model without an external network to predict the linker size. Note, however, that also the unconditional EDM model combined with UniGuide can be adapted to include such predictors.
Table 12: Results for the CrossDocked test set with the joint model trained on the full-atom pocket representation of the pocket for varying guidance scales S. The unconditional model is either controlled by the impainting-inspine technique (DiffSBDD) or UniGuide.
METHON
(1)
VINA Top (2)
(A1
Li (t)
DIVERSITY (1)
RMSD
DIRESDD COND
6,950 1. 2.06
9.120 2.16 -8.115 1.64
0.369
0.21
0.578
0.13
4.562 1 0.89
0.728 0.07
0.000 1. 0.000
DIFSSBD
1/500
6.225 1: 1.77
0.469
0.20
0.573
1 0.11
4.691
1 0.70
0.778 _ 0.04
0.049
0.0.
UNIGUIDE
5.0
1/500
6.346
1.74
8. $.208
1.62
0.4821 0.20
0.570.
0.12
4.718 0.87
0.773 2 0.04
0.040 1.0.01
UNIGUIE
6.0
1:5000
.6.335
2: 1.72
-5.225
à 1.61
1.484
2: 0.30
11571
4 0.12
4.715
0.66
0.775 = 0.04
0.639 0.01
UNKGURE
7.0
1:500
-6.335
1.75
-8.218
1.60
11481
0.19
01571
2 0.12
4.710
0.774 = 0.04
0.639 0.01
UNIGUIDE
8.0
1/500
6.366
2: 1.72
..261 2: 1.57
0.20 0,485
0,570
à: 0.12
4.717
0.66
0.773 0.03
0.039
0.01
DIESRDD
-7.316 2.54
-9.490
0.571 0.19
0.639 0.14
4.808 0.50
0.707 0.09
0.045
UNIQUIDE
-7:205
0.574
0.641
0.706 0.08
0.647 +
UNIGUIDE
7.0
10/50
7.320
2.27
9.514
2.04
0,571 0.19
0.638
0.14
4.822
1 0.47
0.705
0.08
0.047
1 0.01
UNIQUIDS
8.0
10/50
7.258
2,21
9.450
2.01
0.568 0.19
0.641
1.
4.15 1 0.47
0.705
0.09
0.048
0.011
UNIQUIDS
9.0
10/50
-7. 27.26511
2.45
-9.495
2.05
0.577
1 0.19
0.640
1 0.14
4.821 0.447
0.706
0.08
0.049
1 0.01
24

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Table 13: We evaluate the runtime of UniGuide and compare DiftSBDD and DiffSBDD from Schneuing et al. [11]. We report the average time (in seconds) to generate 100 ligands per pocket for the CrossDocked (Ca), Binding Moad (Ca) and Binding Moad (fullatom).
DATASET
MODEL
RUNTIME (8)
DIFISBDD-COND
60 68
CROSsDOCKED (C.)
DIFSBDD
UNIGUIDE
193 6.
DIFS DONDD DIFESRD
54 1: 42
(C.)
UNIGUIDE
104 = 36
DIFESDD
345 + 55
BINDING MOAD (FULL)
DITFSBD
398 95
UNIGUIDE
453 120
Table 14: Additional metrics for the methods discussed Sec. 5.2.
VALIDITY (t)
CONNECTIVITY (f)
UNIQUENESS
NOVELTY
TEST SET
100%
100%:
96.00%
96.88%
CROSS- DOCKED
DIFFSBDD-CONN (C.)
95.32%
80.63%
99.97%
99.81%
DIFFSBDD-COM
97.32%
78.91 9
99.99%
99.91% 9
DIFFSDD (C.)
99.20%
98.14%
99.26%
99.16%
DIFISBDD
97.76%
89.84%
99.94%
99.87%
UNIGUIDE (C.)
99.12%
98.35%
99.50%
99.24%
UNIGUIDE
97.40%
93.18%
99.93%
99.76%
97.69%
38.58
77.55%
BINDING MOAD
DIFTSBDD-COND (C..)
94.43%
77.17%
DIFFSBDD-Com COND
96.20'
63.20%
100%
100%
DIH:SBDD (C.)
98.54%
91.45%
100%
100%
DIFISBDD
94.22%
75.60%
100%
UNIGUIDE (C.)
98.44%
93.12%
100%
99.99%
UNIGUIDE
93.85%
79.95%
100%
100%
F.2 General Fragment Conditions
To assess the performance of UniGuide for the task of FBDD, create experimental setup with the goal of generating ligands conditioned on desired fragments roughly following [13]. We select 10 random protein targets from the Binding MOAD dataset and decompose their corresponding reference ligands using an MMPA-based algorithm [75, 73]. This decomposition results in a set of 40 different scenarios, including separated fragments want link, fragment grow or small functional groups to perform scaffolding. For every set of fixed fragments, we aim to guide the unconditional generation of ligands towards the generation fragments. As the protein is not the target of the guidance, we employ the DiftSBDD-cond model, which is conditionally trained on the rrepreseeetnnnninonn of the protein pocket. For every set of fixed fragments, we generate 100 ligands and use constant guidance scale of 8.
ligand containing the desired
We provide quantitative results for the task of fragment- based drug design in Tab. 15. On the one hand, the task requires the desired fragments to be present in the generated molecule. Thus, we measure the success rate of recovery (Hit Ratio) and the RMSD between the generated fragments and desired fragments. On the other hand, given that the target fragments are met in the generated ligand, the generation has achieve favourable chemical properties, high binding affinity, well high diversity within the set of generated ligands and low similarity to the reference ligand. As the Inpaint mechanism enforces the fragment during generation more strictly, able to achieve better Hit Ratio and RMSD. Nevertheless, UniGuide achieves competitive results but also better VINA docking scores, better properties, and lower similarity compared to the reference ligand.
The FBDD task puts hard constraint on the generated ligands, namely that a set of desired fragments has be present in the generated ligand. However, neither DiftSBDD nor UniGuide can guarantee that the condition fragments are present in the generated samples.
We provide further qualitative results of the generated ligands for the FBDD task in Fig.
25

---

Referencc
Fized Fragmments
DIRSBDD
UniGuide
(2mm))
T7
VINA:
VINA: 11. (7g1))
VINI: 74
VINA: 9D
VINA: 8.2
VINA: 99
VINU:: 9.5
VINA: 6.7
VINA 10.0 (202)
7.5
VINA 10.0 (282)
VINAL
VINAL 02
VINAL
VINA: JO.3
VIRAL -6.0
VINA: 10.3
-108
VINA,
Figure Examples of the generated fragment conditioned ligands.
Table 15: Quantitative comparison between DiftSBDD and UniGuide for the FBDD task on the Binding MOAD (Ca) dataset. As the condition in this FBDD scenario is hard constraint that entails the condition to be exactly present in the generation, we add post-hoc step for both methods where we replace the inpainted or guided parts with the condition atoms. We report mean and standard deviation and highlight the best method in bold.
DIFFSBDD
UNIGUIDE
VINA QED
-7.406
-7.924 +
0.612 0.11
0.639 0.09
SA (t)
0.703 0.11
0.691 0.10
LIPINSKI (f)
4.819 0.28
4.875 1 0.19
DIVERSITY (t)
0.653
0.669
SIMILARITY (L)
0.172
0.02
0.177
1 0.02
VALIDITY (f)
93.35 %
94.41 %
CONNECTIVITY (t)
66.87
68,30 %
G Atom densities in 3D space
Similar to the guidance by the volume enclosed by the molecular surface, UniGuide allows to guide towards multiple point clouds simultaneously. A natural extension of LBDD would be to harness atom densities as described in Zaucha et [82]. Such a setting combines aspects LBDD and SBDD as it provides conditions also on the feature space, yet the source can only be represented by point clouds.
In particular, we anticipate UniGuide to be useful in scenarios where explicit information about advantageous features of the ligand is provided in the form of 3D densities. Examples of this include volumetric densities that indicate beneficial placement of certain atom types, such as oxygen atoms [82] or pharmacophore-liic retrieval of advantageous positions for aromatic rings, as utilised in e.g. Zhu et al. [83]. On technical level, this setting assumes that instead of reference ligand's structure, we only have access (multiple) atom type densities that indicate preferred locations for optimal interaction with the protein. Additionally, instead of conditioning on reference ligand's shape, we could condition on protein pocket's surface, which primarily defines exclusion zones rather than precise atom placement.
26

---

Adapting UniGuide for such scenarios requires only minor adjustments, the protein surface can treated like shapes in standard LBDD, defining an exclusion zone based on proximity to the surface. The atom densities are thresholded to reflect regions of high interest and converted to surfaces using the marching cubes algorithm [84]. To also include feature information, we effectively employ modified condition map similar to Eq. (21) that extends the transformation from the conformation to the configuration space. Moreover, the number of atoms guided by each density is adjusted based on its volume, reflecting the varying influence of each density, and guidance is only applied if atoms are sufficiently close.
We show explorative results for the guided generation of molecules towards desired atom densities using UniGuide in Fig. While our current approach represents a promising first step tackling this task, we acknowledge the potential for further refinement and are eager to explore future improvements within the UniGuide framework.
Fictal
Jeb Drein
Cadliinnt Liacaade
Figure 8: Given source density of oxygens, extend UniGuide generate ligands satisfying the condition.
27

---

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Justification: The claims made in the abstract and introduction reflect the paper's contribution and scope: Sec. 4 details how UniGuide is readily adaptable various tasks in drug design, attesting to the unification provided by the UniGuide framework. Sec. 5 emphasises this aspect through competitive superior performance across various tasks, even when compared to task-specifet baselines.
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Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
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The authors should state which version of the asset used and, if possible, include URL.
The name of the license (e.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, wneeesswthhoode com datasets has curated licenses for some datasets. Their licensing guide can help determine the license dataset.
For existing datasets that are re- e-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
this information is not available online, the authors are encouraged to reach out to the asset's s creators.
13. New Assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [Yes]
Justification: Accompanying the supplementary material, we provide documentation and instructions to navigate and utilise the UniGuide codebase.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset is used.
At submission time, remember anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsourcing and Research with Human Subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
Answer: [NA]
Justification: This work did not conduct research on human subjects or crowdsourcing experiments.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then much detail as possible should be included the main paper.
According to the NeurlPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
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15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/review based the requirements of your country institution) were obtained?
Answer: [NA]
Justification: This work did not conduct experiments where human subject were involved and therefore does not require IRB approvals.
Guidelines:
The answer NA means that the paper does not involve crowdsoureing nor research with
human subjects.
Depending on the country in which research is conducted, IRB approval (or equivalent)
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Reviews:
[{"review_id": "M6yt7OndIs", "reviewer": "Reviewer_YdVq", "summary": "This paper presents a framework for geometric guidance of diffusion models to enable flexible generation for protein and small molecule tasks. Their method is based on self-guidance from geometric conditions. They propose a condition map to map geometric conditions to the latent condition space to guide diffusion. They demonstrate experiments on three main tasks: ligand-based, structure-based and fragment-based drug design.", "questions": "- What is the relation with this work and latent diffusion? Could one similarly encode the geometric conditions using a latent encoder?\n- What is the computational complexity in training these models?\n- What other design tasks could this extend to?", "limitations": "Yes", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper addresses a relevant problem in drug design effectively. There is a need for a general framework for guiding diffusion models for the multitude of protein and small molecule design tasks. This work proposes a novel solution by focusing on geometry-based conditioning, and using a condition map to map different conditions to a common space. They provide extensive experimental evaluation on three major tasks, achieving comparable performance, or outperforming recent methods.", "weaknesses": "A key benefit of this approach is the generalizability of the method. The main concerns I have are in relation to this. Regarding training the model, can the authors provide additional details on the training? For example, are all three tasks trained with different conditioning to guide the model, together? Or is one model trained separately for each task? What is the effect of training on multiple tasks together? For example, if one model is trained per task, then it is difficult to see the benefit of this approach, other than in the conditioning map.\n\nIn the baseline experiments, I feel that there are some related work missing on works that condition diffusion models. For example, how would a simple conditioning mechanism, such as the ones used in the image-text generation literature, fare against this approach? How would this method compare to other latent diffusion models, such as [1-2]? It seems there are a multitude of latent diffusion models for generation out there, I find it difficult to compare those with this. The related work section also does not contrast this work with others in great detail. \n\n### References\n[1] McPartlon, Matt, et al. \"LATENTDOCK: Protein-Protein Docking with Latent Diffusion.\"\n[2] Watson, Joseph L., et al. \"De novo design of protein structure and function with RFdiffusion.\" Nature 620.7976 (2023): 1089-1100.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the feedback and positive evaluation of our method! We provide detailed answers in the following. \n\n&nbsp;\n\n> Additional details on training required for UniGuide’s generality\n- We highlight that **UniGuide does not require extra training** as it controls the generation of pretrained unconditional diffusion models during inference using guidance. \n- Therefore, Uniguide can be directly applied to a suitable (unconditional) model, i.e. a model that matches the configuration space required for the task and is trained on a fitting dataset (e.g. ZINC). We discussed this in the limitations, but we will ensure that this aspect is clearly conveyed in the updated manuscript.\n- Drug design tasks have varying requirements. SBDD and FBDD need protein information, while LBDD and linker design do not. Therefore, the underlying model to which we apply UniGuide varies with the required configuration: We use the unconditional protein-ligand model from [1] for SBDD and FBDD and the molecular generative models ShapeMol or EDM for LBDD and linker design.\n- In summary, UniGuide’s benefit is additive: It does not require a specialised model (no extra training), and the same model can be applied to multiple tasks.\n\n> Comparison with simpler conditioning mechanisms? \n- Controlling the generation of diffusion models using guidance in combination with additional classifiers/regressors is common for the image and text domains [7]. In contrast, UniGuide is a self-guiding [6] approach (Eq.12) that does not require additional models to control the generation, unlike [7]. Another key difference is our **focus on the molecular domain, enabling unified guidance while respecting the requirements of molecular structures: (1) geometric conditions and (2) equivariance**.\n- The condition map is the central element in achieving this. It maps from the space of source conditions S to the configuration space Z (the diffusion model’s output space), realising (1), and maintaining equivariant updates (2) when satisfying Theorem 4.1.\n- We compare to (i) conditionally trained diffusion models and (ii) an inpainting-inspired [1] technique for SBDD and FBDD and show that UniGuide is generally favourable, see e.g. Tab.2. \n- For LBDD, UniGuide is the first method to successfully tackle this task purely at inference time using the surface condition map.\n\n> Q: Computational complexity? \n- Inference: \n    - The computation cost associated with UniGuide results from computing the guidance gradients at inference time, see Eq.15. \n We report runtime comparisons in App.E.2. UniGuide is slightly slower than the inpainting-inspired method [1]. At the same time, the DiffSBDD-cond model provides a baseline for pure sampling without guidance as the computational cost for controlled generation was already invested upfront for the conditional training (which is much higher).\n- Training:\n    - Details on the unconditional training of EDM and ShapeMol[U] are provided in App.C and App.D.1, respectively. For the SBDD experiments, we use DiffSBDD checkpoints, as provided by the authors [1]; see App.E.2.\n\n> Q:Relation with latent diffusion models? Could one encode geometric conditions using a latent encoder?\n- UniGuide can readily be applied to guide a latent diffusion model, for example, GeoLDM [4] instead of EDM [5].\n- In the special case when the source condition is a molecular structure ($S=Z$), one could use the encoder of the latent diffusion model to map the condition to the latent space and guide with UniGuide there.\n- In the general case of $S \\neq Z$, a possible solution is to leverage the decoder D of the respective latent diffusion model and keep the condition map in the data space. That is, instead of computing $C(s, \\hat z_t)$, one estimates the clean latent code and applies the decoder afterwards: $C(s, D(\\hat z_t))$.\n\n> Q: Does UniGuide extend to other tasks? How does it compare to [2-3]?\n\nUniGuide also applies to the domains presented in [2-3]. We did not include them in the current version of the manuscript as they focus on docking and protein generation only, while we focus on drug discovery centred around small molecules.\n- However, we checked the mentioned papers and would like to share some ideas and results on how the presented tasks can be accomplished with UniGuide:\n    - In the context of docking [2], UniGuide could be used to condition on information about the protein complex. Contact information, for example, could be leveraged by guiding to specific positions of the C-a atoms. Coarser positional information, cf. Fig.G.1 [2], could be done in a similar fashion to the shape-based generation presented for LBDD.\n    - Compared with the settings from [3], **UniGuide can be used as an alternative to generate symmetric proteins**. We adopted this idea and chose the C8 symmetry for this PoC. In particular, we designed a pie-like volume element that resembles the required angles and guided the protein generation with the surface condition map from Eq.21. We present the results of this experiment in Fig.2 in the pdf.\n- Additionally, as prompted by reviewer D4nw, we expand the exploration of Density-based Drug Design in Fig. 1 of the PDF.\n\n&nbsp;\n\nWe hope that our answers sufficiently clarify the raised questions. We are thankful for the reviewer’s suggestion to investigate the protein settings and are excited about our results for generating symmetric proteins. \n\n&nbsp;\n\n[1] Schneuing et al. Structure-based Drug Design with Equivariant Diffusion Models\n\n[2] McPartlon et al. LATENTDOCK: Protein-Protein Docking with Latent Diffusion\n\n[3] Watson et al. De novo design of protein structures and function with RFdiffusion\n\n[4] Xu et al. Geometric latent diffusion models for 3d molecule generation\n\n[5] Hoogeboom et al. Equivariant diffusion for molecule generation in 3d\n\n[6] Song et al. Loss-guided diffusion models for plug-and-play controllable generation\n\n[7] Bansal et al. Universal guidance for diffusion models", "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": "", "extra_scores": {}}, {"review_id": "5Jioh4cacW", "reviewer": "Reviewer_cfg3", "summary": "The paper introduces UniGuide which is a general framework for conducting conditioning over the unconditional molecule diffusion models during inference. To achieve this, Uniguide introduced a concept called a condition map for different applications. With a condition map,it could control the score function by adding a task-related gradient term for generating samples with desired properties. The experiment has been conducted over 3 settings of SBDD, FBDD, LBDD to demonstrate the effectiveness of the proposed method.", "questions": "refer to above", "limitations": "No", "rating": 5, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The paper is generally well-written. The motivation is clear and important to the broad audience for taking usage of unconditional models to different complex scenarios. \n\n2. The paper utilizes extensive experiment settings. I appreciate the efforts to conduct experiments in all the SBDD, FBDD, and LBDD settings.", "weaknesses": "1. However, the paper's contribution is hard to evaluate. Though the author claims a new general framework for Uniguide, the form takes exactly as a gradient guidance form for diffusion models which has been explored in the previous literature and following ups [1]. Hence, the key contribution, given in the previous works,  limits to a direct application of gradient-based guidances of molecule diffusion to different scenarios. I would like the author to clarify more about the contribution. \n\n2. The important related works are missing such as [1,2]. I suggest the authors do a comprehensive review over the relevant literature. \n\n[1] Equivariant Energy-Guided SDE for Inverse Molecular Design. ICLR 2023\n[2]Training-free Multi-objective Diffusion Model for 3D Molecule Generation ICLR 2024", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We would like to thank the reviewer for their valuable feedback and will address the raised concerns in our answer below.\n\n&nbsp;\n\n > However, the paper's contribution is hard to evaluate. Though the author claims a new general framework for Uniguide, the form takes exactly as a gradient guidance form for diffusion models which has been explored in the previous literature and following ups [1]\n\n- We acknowledge that UniGuide builds upon the existing framework of gradient-based guidance for diffusion models. However, our primary goal was to **develop a method capable of conditioning on general geometric information, a capability absent in previous work**. We achieve this through two key innovations: self-guidance and the condition map.\n\nKey Differentiators:\n- Condition Map: **UniGuide leverages a novel condition map to incorporate diverse geometric information**, such as protein structures, molecular fragments, and molecular surfaces, as guidance conditions. This is a significant departure from previous work like [1, 2, 3], which are limited to conditioning only on specific (quantum) properties. \n- Self-guidance: UniGuide is a self-guiding approach that modifies the reverse process of the diffusion model without relying on additional networks to guide the generation, similar to prior work [5]. This highlights the flexibility of UniGuide as it does not require additional training (neither training a specialised conditional diffusion model nor training additional networks for guidance). This is unlike prior work [1] that requires training additional regressors to guide the generation.\n- Property-Based Conditioning: In principle, UniGuide can also perform (quantum) property-controlled generation. As this task focuses on global graph properties, it would require additional regressors. \n     - EEGSDE [1], on the one hand, computes the guidance loss between a condition property value $\\mathbf{c}$ and the output of a property prediction network that is finetuned over different noise levels of the diffusion process $\\mathbf{m}_{\\theta}(\\mathbf{z}_t,t)$. \n     - In contrast, UniGuide uses a property regressor trained on clean samples, leveraging a clean approximation ( $\\mathbf{\\hat{z}}_t$ ) of the noisy data ( $\\mathbf{z}_t$ ) for guidance. This approach, explored in [2], differs from our focus on self-guidance. While previous studies [1,2,3] explore property-based conditioning with various conditioning mechanisms, our work investigates self-guidance without relying on external regressors or classifiers, and its broad application across various drug discovery tasks.\n\n- Multiple Conditioning: We further indicate that, unlike prior works [1,2], **UniGuide can support conditioning both on geometric conditions (scaffolds, proteins or shapes) and global graph properties (quantum properties)**, purely during inference. However, this requires additional property regressors [2].\n\n- Motivation for new drug discovery strategies: Inspired by the performance on the LBDD task, we further motivate the applicability of UniGuide for the generation of molecules given molecular densities, see App.G and our detailed answer to Reviewer D4nw. We further provide a qualitative example in Fig.1 in the attached PDF.\n\nUniGuide is Not a \"Direct Application\": Consequently, we can confidently state that our work does not merely constitute a \"direct application\" of gradient-based guidance. **UniGuide introduces fundamental innovations that enable geometric conditioning**, unlocking novel applications and expanding the capabilities of controlled molecule generation.\n\n> The important related works are missing \n- The reason why we omitted the discussion on property-based conditioning is that the current self-guidance formulation of UniGuide does not support drug discovery tasks involving global graph properties. However, it is possible to combine UniGuide with classifier-guidance to enhance the generated molecules' quality for different downstream drug discovery applications.\n- We acknowledge that the omission of this discussion may have led to some confusion. We will incorporate the suggested prior works [1, 2] into the related works section and describe how they differ from UniGuide.\n\n&nbsp;\n\nWe hope that the we were able to appropriately adress reviewer's concerns and are looking forward to a constructive discussion.\n\n&nbsp;\n\n[1] Bao et al. Equivariant energy-guided sde for inverse molecular design\n\n[2] Han et al. Training-free Multi-objective Diffusion Model for 3D Molecule Generation\n\n[3] Hoogeboom et al. Equivariant diffusion for molecule generation in 3d\n\n[4] Dhariwal et al. Diffusion models beat gans on image synthesis\n\n[5] Song et al. Loss-guided diffusion models for plug-and-play controllable generation", "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": "", "extra_scores": {}}, {"review_id": "yBz0ESyPWx", "reviewer": "Reviewer_ZcJd", "summary": "This paper proposed a method named UniGuide for conditional molecular generation with unconditional diffusion models, without the need of additional training and parameters. The proposed framework is an extension of self-guided diffusion models on the conditional molecular generation task. The authors designed different condition maps C: S x Z $\\rightarrow$ Z for ligand-based generation and structure-based / fragment-based generation, enabling guidance from conditions in a unified fashion.", "questions": "See the weaknesses above.", "limitations": "N/A", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "* The paper is generally easy to follow and well-written\n* The theoretical justification is provided and oblation studies / visualization results are sufficient", "weaknesses": "* Technical contribution\n    * My biggest concern is on the superiority of the proposed method over other conditional sampling methods. E.g.  the special case of S = Z can be implemented with inpainting technique; the shape-based generation can also be implemented with some technique similar to classifier guidance (e.g. the validity guidance used in [1][2]) by designing a loss function based on denoised datapoint. However, the authors didn't discuss about the superiority of their method with sufficient experimental supports. \n    * Limitation: The performance is strongly relied on the based unconditional model.\n\n* Clarification\n    * I don’t think the  approximation of Eq 10 makes much sense to me: f approximates the clean data point, then how could the condition c be a Gaussian distribution taking this clean data point as the mean?  I think the concept of condition c $\\in$ Z in this paper is closer to datapoint satisfying condition c, or there should be another mapping from the data space to the condition space. \n    * Eq 17 doesn’t strictly follow the definition of the condition map:  c and z should have the dimension of n x (3 + d) — Eq (18) should have corresponding index selection / mask operations. \n\n* Experiments\n    * In 5.1 Ligand-based drug design, why don’t the authors compare their model with conditional EDM? How could UniGuide (shapeMol), a conditional model with soft constraints, outperform Cond-Shape2Mol?\n    * In 5.3 Fragment-based drug design, I think it’d better also compare UniGuide with an inpainting version of other baselines.\n\n\nReferences:\n\n[1] Peng, X., Guan, J., Liu, Q., & Ma, J. (2023). Moldiff: Addressing the atom-bond inconsistency problem in 3d molecule diffusion generation. arXiv preprint arXiv:2305.07508.\n\n[2] Guan, J., Zhou, X., Yang, Y., Bao, Y., Peng, J., Ma, J., ... & Gu, Q. (2023). DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design. In International Conference on Machine Learning.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their valuable feedback and will address their concerns below. \t\n\n&nbsp;\n\n> Superiority of UniGuide and insufficient experimental support\n\nUniGuide's appeal builds upon multiple aspects:\n - No Training: UniGuide is based on guidance, and as such, it **does not require any additional training but achieves the desired sampling behaviour at inference time**\n - The unification aspect of UniGuide: **Unconditional models can readily be adapted to new settings via UniGuide**. This adaptation effectively reduces to the definition of a condition map C, which can be non-differentiable. To support this, we guide an unconditional EDM model for the LBDD task (Tab.1) as well as the Linker Design task (Tab.3) and show that we outperform specialised approaches.\n - The special case of $S=Z$ (not the general case!) can be addressed using techniques based on inpainting. However, UniGuide leads to better or equal performance, making it favourable over inpainting. This is supported across our experiments, such as in Tab.2 or App.F.2.\n - Extensive experimental support: We benchmark UniGuide against specialised non-diffusion and diffusion-based models (including conditional and guidance-based alternatives) across tasks involving geometric conditions. Our results prove that **UniGuide provides better or on-par performance, indicating that controlling unconditional models with UniGuide is effective, simple, and easily extended to novel settings**. Yet, we acknowledge the need for a more explicit discussion and refer the reviewer to our general response for further clarification on SBDD, LBDD (where UniGuide excels), and FBDD (see also the response to reviewer YA7u).\n\n> Shape-based generation via technique akin to validity guidance\n- We agree that the proposed loss used for validity guidance [1] could be adjusted to the LBDD case, and we thank the reviewer for pointing this out.\n- Yet, **UniGuide is more general and decouples the surface computation (input to the condition map) and gradient computation**, which is consistently applied to the L2 loss between the clean estimate and the target condition.  \n- This decoupling has multiple implications:\n    - Due to the loss formulation, the condition map does not have to be differentiable, making it agnostic to how the surface points are computed and, therefore, more flexible.\n    - At the same time, the condition map follows an explicit geometric intuition, which makes it easily adjustable to novel scenarios. This aspect is especially well reflected in the new experiments discussed in our general response. We guide towards a volume reflecting the symmetry requirement to generate symmetric proteins.\n- In our general response, we discuss incorporating drift terms into UniGuide (akin to validity guidance) for SBDD. As part of this addition, we will conduct experiments to compare an adjustment of validity guidance with our surface condition map. We will share the results as soon as they are available.\n\n> Limitation: Reliance on the base model\n- While UniGuide's performance is inherently tied to the performance of the underlying base model (as noted in our limitations), **this connection also has a positive effect as it encourages research on unconditional generation**. Our experiments show that UniGuide can directly translate improvements to better task-specific performance. UniGuide also facilitates the application of these models to diverse downstream tasks, broadening their utility.\n\n> Eq10 does not make much sense\n\n- We apologise for the confusion caused by the poor presentation of Eq.10.\n- In the current manuscript, we missed to specify that the condition $c$ must lie in the same space as the samples $z\\_t$ (the configuration space). Only this assumption makes the Gaussian approximation possible. To clarify this, we will add further explanations near Eq.10.\n- We would like to highlight that we discuss and lift this assumption on the condition $c$ in our method section (Sec.4). Note that the condition map $C$ serves as a transformation that takes the source condition $s$ and the clean approximation of $z\\_t$ as inputs, and outputs a suitable target condition $c$ that lies in the configuration space and can be used directly in the guidance loss presented in Eq.14/15.\n\n> Eq.17 does not match the definition of C\n\n- In Eq.17, we define the condition map as $C(s, \\hat{z}^{\\mathcal{A}}\\_t)=C(\\tilde{z}, \\hat{z}^{\\mathcal{A}}\\_t)$, where $\\tilde{z}\\in Z$ is a configuration that specifies $m<N$ nodes (for $m=N$ there is no point in guidance). \n- In order to match the dimension of the clean data estimate $\\hat{z}\\_t$ with $\\tilde{z}$, we subset $\\hat{z}\\_t$ to $m$ nodes as indicated by the superscript $\\mathcal{A}$ in the condition map.\n- For example, for SBDD, the source condition is a protein with $m= N^{P}<N$ nodes.\n- While we believe Eq.17 and its definition are consistent, we would appreciate further clarification if we have overlooked any aspects.\n\n> In 5.1 Ligand-based drug design, why do the authors not compare their model with conditional EDM? \n\nIn our general response, we clarify our reasoning for the LBDD evaluation and hope that our answer explains why we did not compare UniGuide (EDM) to conditional EDM. \n\n> How could UniGuide (shapeMol), a conditional model with soft constraints, outperform Cond-Shape2Mol?\n- We believe that what is meant by \"Cond-Shape2Mol\" maps to the conditional ShapeMol [2]. We followed this suggestion and added UniGuide (ShapeMol) to our comparisons; see Tab.3 (PDF).\n\n> For FBDD, add inpainting comparison\n- We added this in Tab.2 in the PDF and would refer to our general response for additional details on this setting.\n\n&nbsp;\n\nAgain, we thank the reviewer for their constructive comments, which have significantly improved our work.\n\n&nbsp;\n\n\n[1] Schneuing et al. Structure-based drug design with equivariant diffusion models\n\n[2] Chen et al. Shape-conditioned 3d molecule generation via equivariant diffusion models", "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": "", "extra_scores": {}}, {"review_id": "Qq3CRdJ4ut", "reviewer": "Reviewer_YA7u", "summary": "This paper proposed a training-free framework for guided diffusions in unconditional molecular generation. UniGuide applies to a wide range of design tasks such as SBDD, FBDD and LBDD, unified by the proposed condition map, which projects from the product space of conditional input that lies in general geometric space to some favorable datapoint in the data space that diffusion operates within.", "questions": "- The condition map works similarly to molecular translation or some form of retrieval given conditional inputs. How would the authors compare to those methods?\n- For SBDD, the authors only reported QVina Dock scores in the main results. However, SBDD models have been criticized for inaccurate structure modeling [1]. It seems to me that Vina Score and Vina Minimize used in [2] would serve as a better indicator for the pose quality. Can the authors also include these metrics in their results?\n\n[1] Benchmarking Generated Poses: How Rational is Structure-based Drug Design with Generative Models?\n\n[2] DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design", "limitations": "See above.", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "- The idea of condition map that unifies different downstream tasks is novel.\n- This paper is generally easy to follow.", "weaknesses": "- In all tables, the authors claimed to highlight the best \"diffusion-based approach\" in bold, which seems misleading since there are also non-diffusion baselines. I would recommend the authors to reconsider this style of presentation in order to faithfully reveal the general performance.\n- After checking other baseline results, UniGuide seems not so competitive in downstream tasks such as LBDD and linker design in FBDD. This casts doubt on its effectiveness.\n- There are a number of important baselines missing, e.g. DecompDiff [1] and IPDiff [2] for SBDD tasks, and LinkerNet [3] for LBDD.\n\n[1] DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design\n\n[2] Protein-Ligand Interaction Prior for Binding-aware 3D Molecule Diffusion Models\n\n[3] LinkerNet: Fragment Poses and Linker Co-Design with 3D Equivariant Diffusion", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their constructive feedback regarding our manuscript, particularly regarding the presentation and interpretation of UniGuide. We believe we can address these concerns effectively, as detailed in the following answers. \n\n&nbsp;\n\n> Only highlight the best diffusion-based approach \n- We are happy to revise the updated manuscript's presentation style as the reviewer suggested.\n- We want to emphasise that we never intended to mislead the reader by highlighting the results in a way that favours UniGuide. We are confident in the benefits provided by UniGuide and agree that they should be presented without ambiguity.\n\n> UniGuide seems not so competitive in LBDD and Linker design in FBDD tasks\n- Clarifications on LBDD performance\n    - We stress that \"on-par\" performance for UniGuide compared to specialised approaches is a significant achievement, as our method imposes no constraints or additional training. The general response provides clarifications on LBDD performance and the reasoning behind the experimental settings. We highlight that **UniGuide achieves very high shape similarity and low graph similarity**, even though it does not rely directly on the reference structure (as in SQUID).\n- Clarifications on FBDD (Linker design) performance\n    - We agree that UniGuide performs on par with DiffLinker overall in the linker design task and does not strictly outperform it. Yet, we want to emphasise again that **we simply guide the sampling of an EDM [1] model that was not optimised for linker design** (unlike DiffLinker, which is a conditional model limited to the linker design task only). In Fig.4 and App. F.2, we showcase how UniGuide can be flexibly adapted to more tasks such as scaffolding or fragment growing.\n    - Despite not being trained explicitly for linker design, UniGuide(EDM) performs competitively with DiffLinker: Our method generates the most diverse linkers (Uniqueness) and successfully recovered nearly 60% (Recovery) of the actual linkers from the test set. While baseline methods may achieve higher recovery rates, they produce less diverse solutions. Moreover, UniGuide (EDM) generates more complex structures as measured by the number of rings. However, this also leads to a slightly worse SA score as these molecules are not as easily synthesisable.\n    - Another advantage of UniGuide not relying on extra training for the linker design task is that it is **agnostic to the fragmentation procedure used to obtain the condition fragments**. This means that UniGuide will generalise to unseen fragments if the underlying molecule fits within the training distribution.\n    - We realise that the original manuscript lacked clarity on these aspects, which may lead to misunderstandings. In the updated version, we will better contextualise the FBDD results.\n\n> Additional baselines\n- SBDD:\n    - We include DecompDiff and IPDiff in the updated version of the manuscript as requested by the reviewer. Furthermore, we are happy to include additional Vina metrics to indicate the pose quality better. Please refer to Tab.1 in the attached PDF. We have also provided additional experimental details and comparisons to different baselines in the general response. \n- FBDD: \n    - We thank the reviewer for pointing us towards the LinkerNet work. Like DiffLinker, LinkerNet is a conditional model that is additionally able to model fragments with more degrees of freedom, i.e. their pose and centre of mass. Since this is also reflected in their experimental setup (LinkerNet can predict the condition fragment poses, the baselines randomly rotate them), it is not directly comparable to the experiments conducted in Table 3. However, this is an exciting addition to the linker design task, which can be readily implemented with minor adjustments to the condition maps presented by UniGuide. We will investigate this addition for inclusion in the updated version of the manuscript.\n\n> Q: Connection to retrieval and molecular translation\n- Comparison to molecular translation: While UniGuide's primary focus is novel drug design with geometric constraints, its adaptability allows for future exploration of molecular translation in 3D, similar to existing 2D approaches [3,4]. This could include, for example, optimising a molecule's properties while preserving its 3D shape using the surface condition map. However, this would necessitate property regressors and the combination of UniGuide with classifier guidance.\n- Comparison to retrieval-based methods: Retrieval-based methods, such as shape-based Virtual Screening (VS),  involve retrieving existing data based on predefined criteria or queries, whereas UniGuide focuses on generating new samples based on a predefined condition without involving existing data. Our comparisons for LBDD show that we surpass VS in terms of 3D and 2D similarity (Tab.1). We are curious to explore the inclusion of retrieval-based methods into the condition map in the future.\n\n&nbsp;\n\nWe hope that we have adequately addressed the concerns raised and believe the reviewer's feedback has significantly enhanced the presentation of our results and the experimental section. We look forward to further discussion.\n\n&nbsp;\n\n[1] Hoogeboom et al. Equivariant diffusion for molecule generation in 3d\n\n[2] Schneuing et al. Structure-based drug design with equivariant diffusion models\n\n[3] Jin et al. Hierarchical generation of molecular graphs using structural motifs\n\n[4] Jin et al. Junction tree variational autoencoder for molecular graph generation", "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": "", "extra_scores": {}}, {"review_id": "rcW1Fv9C4O", "reviewer": "Reviewer_D4nw", "summary": "The paper introduces UniGuide, a unified framework for geometry-conditioned molecular generation using unconditional diffusion models. UniGuide is designed to address the adaptability issues in current molecular diffusion models by providing a general training-free approach via a condition map that transforms complex geometric conditions to match the diffusion model’s configuration space, allowing for self-guidance during the generation process. UniGuide is demonstrated to be effective in various drug discovery tasks, including structure-based, fragment-based, and ligand-based drug design. The framework shows either on-par or superior performance compared to specialized models, highlighting its potential to streamline the development of molecular generative models.", "questions": "1. In the FBDD experiments, can the UniGuide framework also be applied to the DiffLinker model, considering it is diffusion-based backbone?\n2. Based on W1, it is noticed that there is a brief exploration on the density condition in App. G. Given its potential to enhance the model's capabilities, it is suggested to provide additional details about this setting (e.g., task definition, condition mapping) and to reference App. G in the main body of the paper.", "limitations": "The limitation of this paper is well discussed", "rating": 7, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1. The paper introduces a novel, training-free method to guide diffusion models based on expected geometry conditions, enhancing adaptability without additional training overhead.\n2. The framework is thoroughly evaluated across multiple drug discovery tasks, demonstrating its effectiveness.", "weaknesses": "1. The contribution and the generalizability of UniGuide are somewhat overstated. In the Introduction and Figure 1, the available conditions are described in a quite general way, including not only structures and surfaces, but also densities. As this paper mainly focuses on geometry-aware conditions, clarifying the current scope in the introduction and main figures would enhance the paper's accuracy.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We are grateful for the reviewer's insightful feedback and are pleased with the positive comments on UniGuide's novelty and effectiveness for various drug discovery tasks. We would like to clarify the remaining questions and concerns in the following.\n\n&nbsp;\n\n> The contribution and the generalizability of UniGuide are somewhat overstated; the available conditions are described in a quite general way, including not only structures and surfaces, but also densities\n\nWe appreciate the reviewer's feedback and acknowledge the ambiguity between UniGuide's contributions, as shown in Fig. 1, and the empirical evaluations presented in our experimental section. To resolve this ambiguity: \n- We **extended the setting from App.G on density-conditioned guidance as part of our rebuttal** and explain it in more detail down below. \n- We plan to incorporate this novel setting into the final part of Sec.5.1 in the updated manuscript, referring to it as density-based drug design (DBDD), a more challenging task than LBDD.\n\n> Given its potential [of guiding w.r.t. densities] to enhance the model's capabilities, it is suggested to provide additional details about this setting (e.g., task definition, condition mapping) and to reference App. G in the main body of the paper\n\nWe appreciate the reviewer's suggestion and are pleased to provide a more detailed explanation of the technical aspects of the DBDD setting.\n\nTask Definition \n- As motivated in App.G, we anticipate UniGuide to be particularly useful in scenarios where explicit information about advantageous features of the ligand is provided in the form of 3D densities. Examples of this include\n    - a) volumetric densities that indicate beneficial placement of certain atom types, such as oxygen atoms [2] or\n    - b) pharmacophore-like retrieval of advantageous positions for aromatic rings, as utilised in [3]. \n- On a technical level, the DBDD setting assumes this information to be provided as follows:\n    - Instead of a reference ligand's shape, we only have the protein pocket's surface, which primarily defines exclusion zones rather than precise atom placement. Please refer to Fig.1 in the attached PDF.\n    - Instead of a reference ligand's structure, we only have access to (multiple) atom-type densities that indicate preferred locations for optimal interaction with the protein.\n\nCondition Map: Adapting UniGuide for the DBDD scenario requires minor adjustments\n- The protein surface is treated like shapes in standard LBDD, defining an exclusion zone based on proximity to the surface. \n- The atom densities are thresholded to reflect regions of high interest and converted to surfaces using the marching cubes algorithm [4]\n- To include feature information, we employ a modified condition map similar to Eq.21 that extends the transformation from the conformation to the configuration space.\n- Moreover, the number of atoms guided by each density is adjusted based on its volume, reflecting the varying influence of each density, and guidance is only applied if atoms are sufficiently close.\n\n**We have included a new figure in the attached PDF that visually demonstrates qualitative results for this setting**. While our current approach represents a promising first step in tackling this task, we acknowledge the potential for further refinement. We are eager to explore future improvements within the UniGuide framework.\n\n> For FBDD [...], can the UniGuide framework also be applied to the DiffLinker model, considering it is diffusion-based backbone\n\nWhile direct application of UniGuide's FBDD condition map is not possible with DiffLinker, it can be combined with the surface-based Linker Design condition map (App.F.1) to guide linker atom positions.\n- DiffLinker's Modifications: Since DiffLinker fixes condition fragments in space and only learns to diffuse the linker atoms, the model becomes unsuitable for UniGuide's FBDD condition map from Sec. 4.2.\n- DiffLinker's Similarity to EDM: However, DiffLinker's diffusion backbone is very similar to EDM, which we successfully combined with UniGuide for controlled generation in Linker Design, see Tab.3.\n- Compatibility with Surface-Based Conditioning: Moreover, DiffLinker can still be combined with the surface-based Linker Design condition map (App.F.1) to guide the placement of linker atoms towards a specific region between the fragments.\n\n&nbsp;\n\nWe appreciate the positive feedback and are excited to move forward with these improvements. We hope that we have addressed all outstanding concerns satisfactorily and welcome further discussion.\n\n&nbsp;\n\n[1] Hoogeboom, Emiel, et al. Equivariant diffusion for molecule generation in 3d, 2022.\n\n[2] Zaucha, Jan, et al. Deep learning model predicts water interaction sites on the surface of proteins using limited-resolution data, 2020\n\n[3] Zhu, Huimin, et al. A pharmacophore-guided deep learning approach for bioactive molecular generation, 2023\n\n[4] Lorensen, William E., and Harvey E. Cline. Marching cubes: A high resolution 3D surface construction algorithm, 1998", "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": "", "extra_scores": {}}]

Author rebuttal:
We are pleased with the positive feedback on our work, particularly **noting its motivation and its broad and flexible applicability across various drug discovery tasks**.

&nbsp;

We incorporated clarifications and additions to our evaluations -  please refer to the attached PDF and individual responses for detailed information. 

Presentation Style
- We revised the tables’ presentation style as shown in the PDF.
- Initial Distinction: Our quantitative comparisons distinguish between non-diffusion and diffusion-based methods.
- Conditioning Focus: Within diffusion-based methods, we discern the conditioning approaches that control the same backbone. We aim to isolate the effect of different conditioning techniques (inpainting, conditional training, and self-guidance via UniGuide).

LBDD (mainly by YA7u)
- We need to clarify that Tab.1 (Tab.3 PDF) contains various pieces of information that were not presented clearly, obscuring UniGuide's performance:
  - The LBDD task is addressed in different ways: by leveraging only the molecular shape (UniGuide, ShapeMol, VS) or utilising both the shape and the reference structure (SQUID, ShapeMol+g). We indicate this difference in difficulty by a ✓ for methods that only use the shape information and a ✗ for the others.
  - Furthermore, **the ratio metric is the most important** as it combines shape and graph similarities. **UniGuide (EDM) outperforms all other approaches**, highlighting that our approach discovers novel (low graph similarity) ligands satisfying a given shape.
  - Why we include both UniGuide (ShapeMol[U]) and UniGuide (EDM):
    1. To isolate the effect of UniGuide and compare it with the shape-conditioning of ShapeMol, we trained ShapeMol without its conditional part (ShapeMol[U]). The improvements of UniGuide (ShapeMol[U]) over ShapeMol illustrate the performance benefits provided by our guidance. 
    2. Since UniGuide can be applied to any base model, we asked what happens if we use an off-the-shelf EDM model instead of ShapeMol[U]. The substantial performance improvement over both UniGuide (ShapeMol[U]) and ShapeMol, combined with the simplicity of applying UniGuide, demonstrates the effectiveness and benefits of our method.
  - We will revise the updated manuscript to provide a clearer and more detailed explanation of these aspects, ensuring it is better understood.

- Inclusion of UniGuide (ShapeMol) in LBDD (Tab.3 PDF, suggested by ZcJd):  Our application of UniGuide with the surface condition map (Eq. 21) to the conditional ShapeMol demonstrates that UniGuide provides additional benefits also for conditional models. We report this as UniGuide (ShapeMol) in Tab.3 (PDF).

SBDD (Tab.1 PDF, suggested by YA7u&ZcJd)
- As suggested, we added extra metrics: VinaScore, VinaMin, and VinaDock, cf. [1,2].
- We also include DecompDiff [1] & IPDiff [2] as baselines.  
- Due to a discrepancy in the vina metrics (caused by post-processing [3]), we reevaluated UniGuide and the other baselines and report the updated results for Tab.2 (manuscript) in Tab.1 (PDF).
- We draw the following conclusions from the updated results: 
  - Our results, when utilising the same model backbone [3], demonstrate that **UniGuide outperforms alternative conditioning mechanisms**, such as inpainting and conditional training.
  - Furthermore, UniGuide surpasses DecompDiff (no drifts) regarding VinaScore and VinaMin. DecompDiff (all drifts) incorporates additional guidance drifts to enhance the binding affinity. We anticipate that integrating these drifts into UniGuide will further improve performance, and we will present the results for these additions once they become available.
  - We believe that the addition of such drift terms is also crucial for an adequate comparison with IPDiff and DecompDiff, which both add reference and pocket priors to improve the binding affinity specifically.
  - Nevertheless, **UniGuide performs very well just by controlling an off-the-shelf unconditionally trained diffusion model**, proving its generality and effectiveness.

Linker Design (Tab.2 PDF, suggested by ZcJd)
- We implement an inpainting-inspired method for Linker Design and include it in our comparisons, see Tab.2. We use EDM and inpaint the condition fragments, following [3], and observe that the inpainting mechanism alone is not sufficient for the task of Linker Design.
- Additionally, we refer to the experiments in App.F.2, where we evaluate UniGuide for the FBDD (+pocket information) task and compare it to the inpainting technique [3], see Tab.13. These experiments include scaffolding, fragment linking, and fragment growing. Tab.13 demonstrates UniGuide’s favourable performance over inpainting across various metrics. An additional qualitative comparison is available in Fig.7.

**Novel tasks beyond Sec.5** (inspired by YdVq&D4nw)
- Conditioning on densities: We elaborate on the scenario motivated in App.G and refer to this novel setting as Density-Based Drug Design. Fig.1 (PDF) shows how UniGuide can be utilised to condition on densities of atom types or aromatic rings. Please refer to our response to D4nw for extra details.
- Extension to proteins: Even though our main focus centres around small molecules, UniGuide can be used to generate symmetric proteins (C8 symmetry for this PoC), cf. [4]. In particular, we designed a pie-like volume element that resembles the desired angles for the monomer and guided the protein generation with the surface condition map from Eq. 21, see Fig.2 (PDF).

&nbsp;

We are grateful for the opportunity to address the reviewers' concerns and are committed to incorporating their feedback to improve our work further.

&nbsp;

[1] Guan et al. DecompDiff: diffusion models with decomposed priors for SBDD

[2] Huang et al. Protein-ligand interaction prior for binding-aware 3d molecule diffusion models

[3] Schneuing et al. Structure-based drug design with EDM

[4] Watson et al. De novo design of protein structures and function with RFdiffusion

Meta-review: The authors present a new approach for imposing geometrical conditions when sampling diffusion models. The authors illustrate their approach on several tasks relevant to drug design and protein engineering. Reviewers raised several points regarding the presentation and requested new experiments. Many of these were addressed well by the authors during the rebuttal, and they promised to include further results in a camera-ready version. Overall, the paper is interesting and potentially valuable if it is as easy and broadly applicable as noted by the authors. Some reviewers noted that the performance was similar to baselines, suggesting a limited utility of the method. However, the authors have clarified their results and experiments, indicating their approach improves results substantially. My primary personal issue with this paper was the unclear technical presentation, albeit unnecessarily verbose, raising my doubts about its technical rigor.
Decision: Accept (poster)