Unified Guidance for Geometry-Conditioned Molecular Generation

Authors: sirine  ayadi
leon  hetzel
johanna  sommer
fabian  theis
stephan  günnemann
Venue: NeurIPS_cc_2024_Conference
Published: 2024-05-14 17:29:30

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.

Main paper: 
 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] [4] [5] [6] [7] [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 a 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 or slightly altered settings.We address the challenge of adaptability by introducing UniGuide, a method that unifies guidance for geometry-conditioned 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 Figure 1 : UniGuide handles diverse conditioning modalities for guidance, including: (i) a target receptor for SBDD, (ii) additional molecular fragments for FBDD, or (iii) a predefined 3D shape for LBDD. It combines a source condition s ∈ S and the unconditional model ϵ θ (z t , t) within its condition map to enable self-guidance. The flexible formulation of our approach can be generalised to new geometric tasks, for example, conditioning on atomic densities. 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] [13] [14] . With our method, we are able to tackle the same tasks, while overcoming major drawbacks: UniGuide eliminates 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 geometry-constrained 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 geometry-conditoned molecular structures, requiring neither additional training nor external networks used to guide the generation.• We demonstrate UniGuide's wide applicability by tackling various conditioning scenarios in structure-based, fragment-based, and ligand-based drug design.• We show UniGuide's favourable performance over task-specific baselines, highlighting the practical relevance of our approach. 
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] [18] [19] [20] [21] are based on 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 our 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] [26] [27] [28] [29] [30] [31] [32] [33] [34] . However, these methods are limited in modelling the molecules' conformation information and are, therefore, not ideally suited for several drug-discovery settings, such as target-aware drug design. Recently, attention has shifted towards generating molecules in 3D space, utilising variational autoencoders [35] , autoregressive models [36] [37] [38] , flow-based models [39, 40] , and diffusion-based approaches [20, [41] [42] [43] [44] [45] [46] [47] .Conditional generation of molecules Downstream applications of molecular generation can be categorised by their condition modality. In 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] [52] [53] . Igashov et al. [13] expand given scaffolds by generating the molecule around the fixed scaffolds. In a related task of FBDD, linker 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 is often scarce. For this reason, LBDD aims to 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 a reference ligand and use the resulting embedding to train a conditional diffusion model.Question: Does the paper discuss the limitations of the work performed by the authors? Answer: [Yes] Justification: We discuss the limitations of UniGuide in Sec. 4. Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper. • The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be. • The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated. • The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon. • The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size. • If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness. • While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. 
controlling the generation of diffusion models: 
 Diffusion Models [9, 57] learn a Markov Chain that involves a forward process to perturb data from a distribution q(z) and learn to reverse the process to generate new samples from a tractable prior, for example, a normal distribution. Given a data point sampled from the true underlying distribution, z data ∼ q(z), the forward process q(z t |z t-1 ) gradually adds Gaussian noise:EQUATIONwhere {β t ∈ (0, 1)} T t=1 defines a variance schedule. Defining the forward process this way, one can readily sample from q(z t | z data ):EQUATIONwith α t = 1 -β t and α t = t i=1 α i . Since the time-reverse process q(z t-1 |z t ) depends on z data , which is not available at generation time, it is approximated by modelling p θ (z t-1 | z t ):EQUATIONwhere the mean µ θ is parameterised by a noise-predicting neural network ϵ θ in the form of:EQUATIONThe model ϵ θ is trained to optimise the variational lower bound through the simplified training objective:EQUATION(5)Self-guiding diffusion models Using Bayes' rule, the conditional probability p θ (z t | c) given a condition c can be expressed asEQUATIONThis allows us to decompose the score function as follows:EQUATIONwhere the second term is used for guiding the unconditional generation, with S > 0 controlling the guidance strength. Using that∇ zt log p θ (z t ) = -(1 -α t ) -1 2 ϵ θ (z t , t) [22], we can rewrite the score function from Eq. ( 7) and identify the modified noise predictor εθ :EQUATIONThe modified mean function μθ then follows from the modified version of Eq. ( 4), enabling us to sample from p θ (z t-1 | z t , c) ∼ N μθ (z t , t, c), σ t I :EQUATIONwhere λ(t) = (α t ) -1 2 β t S balances the conditional update. Eq. ( 9) requires sampling from log p θ (c | z t ) to which we do not have access. Assuming the condition c lies in the same space as z t , we can follow Kollovieh et al. [58] and approximate log p θ (c | z t ) as a multivariate Gaussian distribution:EQUATIONwhere f θ (z t , t) approximates the clean data point, enabling to estimate the condition in data space. Using Eq. ( 2), we can readily predict the clean data point given the noisy sample z t viaEQUATION)With this, the guiding term becomes a direct differentiation of the squared error with respect to the noisy sample z t :EQUATION)By directly leveraging the prediction of the unconditional model ϵ θ , Eq. ( 12) establishes our selfguiding conditioning, thereby defining the self-guided noise predictor εθ :EQUATION)Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?Answer: [Yes] Justification: We discuss in Sec. 4 that the generative process retains equivariance with an appropriately chosen condition map and provide a full proof for this discussion in App. B. 
uniguide: 
 To enable the application of unconditional molecular diffusion models ϵ θ to geometric downstream tasks in drug discovery, we aim to develop a unified guidance framework, UniGuide, see Fig. 1 . Importantly, we seek to enable guidance from arbitrary geometric conditions s ∈ S, where S denotes a general space of source conditions. However, the source conditions s 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 s and target conditions c suitable for guidance. In Sec. 4.1, we start with its general formulation and continue to derive a condition map C Z 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 to derive a task-specific condition map C ∂V for ligand-based drug design.Notation In 3D space, the configuration of molecules, including proteins, can be represented by a set of tuples z = {(x i , h i )} N i=1 ∈ Z, where x i ∈ R 3 and h i ∈ R d refer to coordinates and features of a node z i = (x i , h i ), respectively. The space of configurations is denoted by Z and includes configurations of varying size N . We distinguish between different configuration entities via superscripts, i.e. refer to molecules M and proteins P through z M and z P , respectively. The collection of coordinates x = {x 1 , . . . , x N } ∈ R N×3 ∈ X defines the conformation of a molecule M or protein P. We represent arbitrary geometric conditions with the variable s ∈ S, and conditions that can be used for guidance with the variables c ∈ Z.The concept of a condition map C is essential to our method, enabling guidance from conditions s ∈ S in a unified fashion, where S represents a space of general geometric objects such as structures, densities, or surfaces. These geometric objects do not necessarily match the configuration space Z, i.e. S ̸ = Z, preventing the computation of the guiding score function from Eq. (12) . We overcome this challenge by defining C as a transformation that maps s to a suitable target condition c ∈ Z, which is then utilised for self-guidance.In the most general case, C takes the form ofEQUATIONwhere the source condition s together with a configuration z are mapped to a target condition c ∈ Z.Including the condition map C in the guidance, we obtain our guidance signal:EQUATIONwhere ẑ0 = f θ (z t , t) is the estimate of z 0 given the unconditional model ϵ θ (z t , t) obtained according to Eq. ( 11) and c = C(s, ẑ0 ) is the target condition produced by the condition map. In this formulation, c 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 unconditional generative process. In particular, if the unconditional model ϵ θ is equivariant to a set of transformations G, e.g. rotations and translations, as is common in the molecular domain, we want to retain equivariance also in the guidance signal. Hence, the self-guided model εθ should satisfyEQUATIONfor all transformations G to which ϵ θ is equivariant. Guidance in the special case of S = Z In the case where the source condition s directly defines subset A of m < N nodes of the configuration, i.e. S = 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 = z ∈ R m×(3+d) and refer to the defined subset within the configuration ẑ0 by ẑA 0 . In order to satisfy the requirements on C z, ẑA 0 as stated by Theorem 4.1, we align z with ẑA 0 by using the Kabsch algorithm [59, 60] . Denoting the resulting transformation with T ẑA 0 , we get an ẑ0 -equivariant condition map:EQUATIONTaken together, we can compute the guidance signal based on the following loss L:EQUATIONWe emphasise that although the loss L ẑA 0 , z is computed on the subset A, the gradient, as presented in Eq. (15) , is still computed with respect the full configuration z t .In summary, our method requires only an unconditionally trained model ϵ θ and a suitable condition map C, eliminating the need for additional networks or training. Together, this facilitates unified self-guidance from arbitrary geometric sources. Importantly, the separation of model training and conditioning enables us to tackle tasks even with minimal data, which is crucial in practical scenarios. In the following section, we discuss the wide applicability of UniGuide by illustrating its application to multiple drug discovery tasks.Having introduced both the guidance framework and the condition map, we will continue to discuss how to tackle a set of drug discovery tasks within the UniGuide framework. We start with its application to ligand-based drug design (LBDD), which aims to generate a ligand that satisfies a predefined molecular shape. Ligand-based drug design LBDD aims to generate novel ligands with a similar 3D shape as a reference ligand M ref .In this setting, one operates on the molecule level only since the protein information is assumed to 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 εθ to generate a ligand z 0 with a similar 3D shape but different molecular structure than M ref . With Sec. 4.1 introducing all required concepts, we can readily formulate a surface condition map C ∂V suitable to tackle the task of LBDD, see Fig. 2: To represent M ref 's 3D shape, we identify our source condition s with a set of K points y sampled uniformly from the reference ligand's surface ∂V , y ∈ R K×3 = S. As no features are guided, we formulate C ∂V with respect to the conformation space X = R N ×3 :EQUATIONwhere x0 denotes the conformation of the clean data point estimation ẑ0 as computed by Eq. ( 11). EQUATIONFinally, the individual components c x,i of the target condition compute as follows:EQUATIONwhere d denotes the distance to the surface, d = ∥ ȳixi ∥ 2 , and α the required distance to the surface. Note that the target condition c x represents a valid conformation inside the surface ∂V , and that C ∂V effectively bridges spaces from S to X . Consequently, when using C ∂V , the guidance signal is derived from Eq. ( 15) with the loss function L(ẑ 0 , y). The full algorithm for guidance using C ∂V is presented in App. D.1.The goal of SBDD is to design a ligand that binds to a target protein pocket s. In this setting, one operates on both the molecule and protein level. Technically, we are interested in generating a ligand z M 0 conditioned on the protein configuration zP . With the unconditional diffusion model ϵ θ (z t , t), z t = (z M t , z P t ), approximating the joint distribution of ligand-protein pairs p(z M data , z P data ), one can readily see that the source condition directly corresponds to the configuration of the protein pocket. Hence, we can use C Z from Sec. 4.1 and identify z with zP . The guidance signal then follows from the loss L(ẑ P 0 , zP ) with c P = C Z (z P , ẑP 0 ) as defined in Eq. (18) . We describe the sampling algorithm for the SBDD task in App. E.1.Fragment-based drug design FBDD aims to design a ligand by optimising a molecule around fragments F that bind weakly to a receptor. Similarly to SBDD, one operates on both the molecule and protein level. Technically, we are interested in generating a ligand z M 0 conditioned on both the protein and the fragment configuration, zP and zF , respectively. Considering the same kind of unconditional model ϵ θ (z t , t) as in SBDD, we can use C Z from Sec. 4.1. Only now, we identify z with both zP and zF and write zA with A = P ∪ F. Using Eq. ( 18), the guidance signal directly follows from L(ẑ A 0 , zP∪F ) with c P = C Z (z P∪F , ẑP∪F 0). The sampling algorithm is similar to the one described in App. E.1.Several tasks exist within the FBDD setting [62] [63] [64] [65] . Examples are scaffold hopping [64] , where the core structure of z M 0 has to be generated, but functional groups that interact with the receptor are fixed, or linker design [65] , where the connection between separated fragments has to be optimised through the generative process, see Fig. 5 . 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 zP is discarded. This usually aligns with switching to an unconditional model ϵ θ 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 a version of the surface condition map C ∂V 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 a matching configuration space. We discuss the broader impact of our work in App. A.Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?Answer: [Yes] Justification: The setup of all experimental evaluations is described in App. E, App. F and App. D for the SBDD, FBDD and LBDD tasks respectively, including hyperparameters for UniGuide, dataset preprocessing and inference algorithms. For experimental evaluations performed according to previous work, we reference them accordingly. 
results: 
 In this section, we compare UniGuide to state-of-the-art 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 or even surpasses specialised baseline models, underscoring its practical relevance and transferability to diverse drug discovery scenarios.Dataset Following Chen et al. [14] , we employ the MOSES dataset for the ligand-based drug design task [66] . We evaluate on a test set consisting of 1000 reference ligands, from which the 3D shape conditions are extracted. For every shape condition M ref , 50 samples are generated. We refer to App. D.1 for further details on the evaluation setup.Baselines For the LBDD task, we compare UniGuide to ShapeMol, a conditional diffusion model that is trained by conditioning on 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 C ∂V 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. 1 indicates whether a 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 to 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 LBDD task, we further motivate its applicability for the generation of molecules given atom densities, see App. G. Evaluation The goal of LBDD is to discover novel molecules that fit within a given 3D shape. This can be quantified by a high 3D shape similarity and low graph similarity compared to the reference ligand, as illustrated 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 Sim S /Sim G , which constitutes the most important metric for this task. We follow Chen et al. [14] and further evaluate the mean and maximum shape similarities Sim S and max Sim S , respectively, per reference ligand, measured via the volume overlap between the two aligned molecules. Additionally, we report the graph similarity Sim G defined as the Tanimoto similarity between the generated and reference ligand, and the graph similarity max Sim G of the generated molecule with the maximum shape similarity. Further metrics concerning the quality of the generated ligands are provided in App. D.2.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 it is able to 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 is 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 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-the-art performance on new tasks.Datasets Following Schneuing et al. [11] , 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 on 100 test protein pockets. 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 C α 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-based generation: (i) DiffSBDD-cond, a conditional diffusion model similar to [50] and (ii) DiffSBDD, an inpainting-inspired technique that modifies the generative process of an unconditional diffusion model that jointly generates protein-ligand pairs. Across datasets, both UniGuide and DiffSBDD control the same unconditional ligand-protein 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 as well as the resampling trick [71] , 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-related metrics (Vina Score, Vina Min and Vina Dock), which estimate the binding affinity between the generated ligands and a given test receptor [72] . Additionally, we measure the quality of the generated ligands using two chemical properties: the drug-likeness (QED) and the synthetic accessibility (SA) [66, 73] . Tab. 2 demonstrates that, without additional training or external networks, UniGuide 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, DiffSBDD's inpainting-inspired technique, is not a limitation in practice. Rather, it suggests that utilising self-guidance in combination with a suitable condition map generates wellharmonised ligand-protein pairs. This is also reflected in the properties of the generated ligands, where UniGuide achieves good drug-likeness (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 is even able to improve over the VINA Dock metric of the reference ligand.Datasets & Baselines In the following, we investigate linker design, a 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 DiffLinker [13] , a 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.Figure 5 : For various pocket-conditioned FBDD tasks, we show reference ligands (grey), desired fragments (magenta), and ligands generated by UniGuide (blue).Evaluation Following Igashov et al. [13] , we evaluate the generated linkers and ligands with respect to their properties (SA, 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.Using UniGuide to control the EDM generation enables the successful combination of the condition fragments and the generation of diverse linkers. Even compared to taskspecific models, UniGuide is able to perform competitively across different metrics. Importantly, UniGuide enables the same unconditional model (EDM) to tackle both the linker design task as presented in Tab. 3 as well as the LBDD task as presented in Tab. 1 without additional training. Note that, while DiffLinker is specifically designed to generate 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 as long as the underlying molecule fits within the training distribution. In App. F.2, we 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. 
conclusion: 
 In this work, we present UniGuide, a unified way of controlling the generation of molecular diffusion models towards geometric constraints. UniGuide generalises to a 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 is 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. 
safeguards: 
 Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)? Answer: [NA] Justification: The research discussed in this paper does not require safeguards to be put in place.Guidelines:• The answer NA means that the paper poses no such risks.• Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters. • Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images. • We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort. 12. Licenses for existing assets Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?Answer: [Yes] Justification: Where applicable, we credit and cite owners and authors of previous works and the accompanying codebases or datasets and provide the license under which the assets were made public.Guidelines:• The answer NA means that the paper does not use existing assets.• The authors should cite the original paper that produced the code package or dataset.• The authors should state which version of the asset is used and, if possible, include a 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, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset. • For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided. • If this information is not available online, the authors are encouraged to reach out to the asset's creators. 
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 to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file. 
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 in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper. • We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution. • For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review. 
 
 Appendix: Our research holds the promise of significant contributions to the advancement of 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 Proof. We start the proof by showing that ∥v∥ 2 is invariant to transformations of both z and s.EQUATION2. ∥z -C(s, z)∥ 2 is invariant to transformations s follows immediately:EQUATIONIn a second step, we make use of the fact that for a group of transformations G, it holds that if [76] . From the invariance of ∥v∥ 2 , it follows immediately that ∇ z z -C(s, z) L(•, •) is a G-invariant function, ∇ x L(•, x) is G-equivariantUniGuide guides an unconditional diffusion model given an arbitrary condition and a natural choice for a model operating only on the molecule level is the EDM model as proposed in Hoogeboom et al. [20] .We adapt this model for two tasks presented in this work, namely the LBDD task discussed in Sec. 5.1 and the Linker Design task as presented in Sec. 5.3. For these tasks, we train an unconditional EDM model both on the MOSES dataset [66] in the configuration as 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 as described in Hoogeboom et al. [20] . We run multi-GPU trainings on 4 NVIDIA A100 GPUs until convergence, however, a single NVIDIA A100 GPU is sufficient for this training and will only increase the training time. For inference, we employ the Resampling trick as discussed in Lugmayr et al. [71] with R = 10 resampling steps and T = 100 timesteps. EDM is available under the MIT License.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 and randomly select 1000 samples for validation. The model architecture of ShapeMol[U] is an unconditional version of the ShapeMol model proposed in Chen et al. [14] , and it is 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 a Gaussian distribution centred around every atom 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:EQUATIONwhere d( x, z) is the Euclidean distance, n( x, Q) is the set of n nearest neighbors of x in Q and γ > 0 is a distance threshold. We follow the implementation of Chen et al. [2] for the position correction method by setting γ = 0.2 and only guiding during the first 700 denoising steps.For the shape-conditioned 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 Sim S as the volume overlap between the aligned generated ligand and the condition ligand. For the alignment, we utilise the ShaEP tool [78] .We provide a detailed description of the LBDD sampling algorithm in Algorithm 1.Algorithm 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. For the LBDD task, the guidance strength S is weighted by an exponentially decreasing function βt √ αt . For the guided generation using the unconditional ShapeMol [U] model under the UniGuide framework, we define a scale scheduler that increases with an exponent of 1.01 and weight it with βt √ αt 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 5 to 15. The guidance is applied from the diffusion step 920 to the last timestep 1.We adapt the validity guidance loss from Guan et al. [50] to the LBDD setting. The proposed loss is grounded in the smooth distance function S(x) from Sverrisson et al. [79] , which computes as:S(x) = -σ log N i exp(-∥x t -y i ∥ 2 2 /σ) .This function provides an alternative approach to shape-based generation by deriving an appropriate loss function x S(x), rather than modifying the condition map as proposed by UniGuide. Here, S(x) implicitly defines a surface through S(x) -γ = 0 and points x t inside satisfy S(x t ) < γ.On a technical level, the gradient for validity guidance computes as follows:∇ xt S(x t ) = ∇ xt -σ log N i exp(-∥x t -y i ∥ 2 2 /σ) = 1 exp(. . . ) N i exp(. . . ) ωi ∇ xt ∥x t -y i ∥ 2 2 = 1 ω i ∇ xt N i ω i ∥x t -y i ∥ 2 2 .This gradient formulation is quite similar (up to the weighting) to UniGuide's special case S = Z, as it computes an L 2 loss on a given conformation ({y i }), see Eq. ( 18), meaning that it does not generalise to 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 flexibility in computing surface points. Second, the precise geometric intuition behind the condition map makes it easier to adapt to new scenarios, as demonstrated by our application to generating density-guided molecules.For the empirical comparison, we selected the hyperparameters σ and γ in the surface loss computation to achieve a high DICE score between the implicitly defined surface and the meshes UniGuide utilises for LBDD (σ = 1, γ = 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 performed 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 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 in UniGuide allows for relating the gradient updates directly to the surface, as shown in Eq. ( 21).Algorithm 2: Sampling algorithm to generate a ligand conditioned on a protein pocket zP using the unconditional joint model ϵ θ (z t , t), where z t = [z M t , z P t ], that models the distribution P (z M , z P ). The guidance signal is controlled via the guidance strength S. Note that samples from the generative process p θ (z t-1 |z t ) are assumed to be CoM-free.Require: zP , S z T ∼ N (0, I) {Sample from normal prior} for t = T to 1 doẑP 0 = z P t - √ 1 -ᾱt ϵ P θ (z t , t)/ √ ᾱt {Compute the clean data of the pocket} L = L(ẑ P 0 , zP ) g = (∇ xt L -∇ xt L, ∇ ht L){Compute gradient and substract the CoM}µ t = µ θ (z t , t) -λ(t) • g{Update the mean of the pocket} z t-1 ∼ N (µ t , σ t I) end for return z = (z M 0 , z P 0 )We provide the algorithm for inference in the SBDD task scenario in Algorithm 2.SBDD aims to generate a ligand given a protein pocket: p θ (z M | z P test , t). We adopt DiffSBDD [11] , an unconditional joint diffusion model that approximates the joint distribution p(z M data , z P data ) of generating ligand-protein pairs, where the noise predictor ϵ θ (z M t , z P t , t) is parametrised by EGNN. DiffSBDD 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 ϵ M θ (z M t , z P t , t) and ϵ P θ (z M t , z P t , t) [11] . For the unconditional sampling with the joint model, the number of ligand and pocket nodes is sampled from the joint node distribution p(N M , N P ), measured a training set of (M, P) pairs. During the modified generative process with the inpainting-inspired technique or with UniGuide the number of pocket nodes is set to be equal to the number of nodes in P test , while the size of the ligand is generated from a conditional distribution p(N M | N P ). Since this sampling procedure leads to ligands that are 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 [11] . We utilize the unconditional base models from Schneuing et al. [11] , which are trained on either the C α or full-atom context from the Binding MOAD or CrossDocked datasets. However, we retrain the DiffSBDD model specifically on the full-atom context of the CrossDocked data, as we were unable to reproduce the reported results in this configuration from Schneuing et al. [11] . We find that contrary to 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 DiffSBDD inpainting-inspired approach as well as UniGuide. We train the model on four NVIDIA A100 GPU with a batch size of 2. 8 training epochs take approximately 24 hours. < 5 Å < 5 Å < 8 Å < 7 Å EDGES (POCKET-POCKET) < 5 Å < 5 Å < 8 Å < 4 ÅRepresenting ligands and proteins as graphs Proteins consist of amino acids, where every amino acid is a set of amino (N H), carboxyl (CO), α-carbon atom and a side chain (R) that is specific to every amino acid type [81] . The C α -representation of a protein pocket is a 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 M , z P ) are provided in Tab. 6. We refer the reader to Schneuing et al. [11] for more information on the hyperparameters of the joint model. In addition to Tab. 2, we follow the experimental setup as utilised in Schneuing et al. [11] to compare UniGuideto DiffSBDD, which uses the same base model, in particular. In Tab. 8, we further investigate the advantages of using self-guidance in combinations with UniGuide over both the conditional DiffSBDD model (DiffSBDD-cond) as well as the inpainting-inspired technique 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 M t , z P t ) pairs at denoising step t, the protein pocket P t is replaced with the noised representation of protein context zP t . 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 a technique they call "Resampling". This modifies the reverse Markov chain by moving back and forth in the diffusion process to 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 we evaluate how the unconditional generation of the joint model is improved across different metrics with added resampling steps. We follow Schneuing et al. [11] in using the setting of R = 10 resampling steps and T = 50 timesteps. While DiffSBDD 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 z t with the condition c.The guidance scale S controls the strength of the guiding signal, see Eq. ( 7) and it is weighted by w(t) = β(t)√ αt during the generation. We use a constant scale S for structure-based drug design experiments and evaluate for several guidance scale values in Tab. 9 and Tab. 10 for models trained on the Binding MOAD dataset with C α and full-atom representation respectively. The quantitative evaluation on the CrossDocked data is shown under Tab. 11 and Tab. 12 with additional metrics reported in Tab. 7. For the generation with the C α -models, we generate 100 samples for every test pocket with a batch size of 50. The full generation takes approximately 5 hours for Binding MOAD and 6 hours for CrossDocked. For the DiffSBDD 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 2 to sample with the DiffSBDD model trained on CrossDocked (fullatom).Table 13 : We evaluate the runtime of UniGuide and compare it to DiffSBDD-cond and DiffSBDD from Schneuing et al. [11] . We report the average time (in seconds) to generate 100 ligands per pocket for the CrossDocked (C α ), Binding Moad (C α ) and Binding Moad (fullatom). To assess the performance of UniGuide for the task of FBDD, we create an 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 we want to link, a fragment to 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 of a ligand containing the desired fragments. As the protein is not the target of the guidance, we employ the DiffSBDD-cond model, which is conditionally trained on the (C α )-representation of the protein pocket. For every set of fixed fragments, we generate 100 ligands and use a constant guidance scale of 8.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 to achieve favourable chemical properties, high binding affinity, as well as 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, it is able to achieve a 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 a hard constraint on the generated ligands, namely that a set of desired fragments has to be present in the generated ligand. However, neither DiffSBDD 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. 7 . Table 15 : Quantitative comparison between DiffSBDD and UniGuide for the FBDD task on the Binding MOAD (C α ) dataset. As the condition in this FBDD scenario is a hard constraint that entails the condition to be exactly present in the generation, we add a post-hoc step for both methods where we replace the inpainted or guided parts with the exact condition atoms. We report mean and standard deviation and highlight the best method in bold. 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 al. [82] . Such a setting combines aspects of 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 a) volumetric densities that indicate beneficial placement of certain atom types, such as oxygen atoms [82] or b) pharmacophore-like retrieval of advantageous positions for aromatic rings, as utilised in e.g. Zhu et al. [83] . On a technical level, this setting assumes that 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. Additionally, instead of conditioning on a reference ligand's shape, we could condition on a protein pocket's surface, which primarily defines exclusion zones rather than precise atom placement.Adapting UniGuide for such scenarios requires only minor adjustments, as 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 a 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. 8 . While our current approach represents a promising first step in tackling this task, we acknowledge the potential for further refinement and are eager to explore future improvements within the UniGuide framework. Justification: The claims made in the abstract and introduction reflect the paper's contribution and scope: Sec. 4 details how UniGuide is readily adaptable to various tasks in drug design, attesting to the unification provided by the UniGuide framework. 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Decision: 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.

Reviews: review: paper_summary: paper_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.
strength_weakness: strength_weakness: 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.

In 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. 

### References
[1] McPartlon, Matt, et al. "LATENTDOCK: Protein-Protein Docking with Latent Diffusion."
[2] Watson, Joseph L., et al. "De novo design of protein structure and function with RFdiffusion." Nature 620.7976 (2023): 1089-1100.
questions: questions: - What is the relation with this work and latent diffusion? Could one similarly encode the geometric conditions using a latent encoder?
- What is the computational complexity in training these models?
- What other design tasks could this extend to?
limitations: limitations: Yes
paper_summary: paper_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.
strength_weakness: strength_weakness: 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. 

2. The important related works are missing such as [1,2]. I suggest the authors do a comprehensive review over the relevant literature. 

[1] Equivariant Energy-Guided SDE for Inverse Molecular Design. ICLR 2023
[2]Training-free Multi-objective Diffusion Model for 3D Molecule Generation ICLR 2024
questions: questions: refer to above
limitations: limitations: No
paper_summary: paper_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.
strength_weakness: strength_weakness: * Technical contribution
    * 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. 
    * Limitation: The performance is strongly relied on the based unconditional model.

* Clarification
    * 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. 
    * 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. 

* Experiments
    * 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?
    * In 5.3 Fragment-based drug design, I think it’d better also compare UniGuide with an inpainting version of other baselines.


References:

[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.

[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.
questions: questions: See the weaknesses above.
limitations: limitations: N/A
paper_summary: paper_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.
strength_weakness: strength_weakness: - 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.
- 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.
- There are a number of important baselines missing, e.g. DecompDiff [1] and IPDiff [2] for SBDD tasks, and LinkerNet [3] for LBDD.

[1] DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design

[2] Protein-Ligand Interaction Prior for Binding-aware 3D Molecule Diffusion Models

[3] LinkerNet: Fragment Poses and Linker Co-Design with 3D Equivariant Diffusion
questions: 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?
- 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?

[1] Benchmarking Generated Poses: How Rational is Structure-based Drug Design with Generative Models?

[2] DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design
limitations: limitations: See above.
paper_summary: paper_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.
strength_weakness: strength_weakness: 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.
questions: questions: 1. In the FBDD experiments, can the UniGuide framework also be applied to the DiffLinker model, considering it is diffusion-based backbone?
2. 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: limitations: The limitation of this paper is well discussed

Comments: title: Thank you for your response
Technical difference between UniGuide and validity guidance
Thanks for your response
Highlighting methodological differences and superiority of UniGuide
Thank you
Thank you and additional clarifications
Clarification on performance and broader impact of UniGuide
Additional results posted as official comment
Additional Analyses for SBDD and LBDD
comment: Thank you very much for the kind words; we are grateful for an increased score and are excited about the positive feedback on the novelty of the UniGuide framework. We are pleased to hear that you found our additional clarifications on gradient-guided generation satisfactory, which will be included in the camera-ready version of the paper.

Best regards,

The Authors
We thank the reviewer for engaging in the discussion and raising this important clarifying question. It is correct that both UniGuide and the validity guidance from [1] compute the loss in coordinate space. 

However, UniGuide's condition map explicitly maps the condition to target points related to the surface, expressed as $c = C(s, \hat{x}_t)$, where $s$ represents the surface and $\hat{x}_t = f\_\theta(x_t, t)$ is the clean data conformation approximation. In contrast, [1] leverages the shape descriptor $S(x_t)$ to decide if a point $x_t$ is inside the volume but then does not use the surface for the gradient update but regresses against all surface-generating points.

Note that [1] relies on this differentiable function $S(x)$ to implicitly define a surface via $S(x)-\gamma=0$. For a point $x_t$ that satisfies $S(x_t)<\gamma$, the gradient computes as follows:  

$$
\begin{aligned}
\nabla_{x_t} S(x_t) = \nabla_{x_t} \Big [ -\sigma \log \Big ( \sum_i^N \exp(-\|x_t-y_i \|_2^2 / \sigma ) \Big ) \Big ] \\
\end{aligned}
$$

$$
\begin{aligned}
\qquad \qquad & = \frac{1}{\sum \exp(\dots)} \sum\_i^N \underbrace{\exp(\dots)}\_{\omega_i} \nabla\_{x_t} \|x_t-y_i \|_2^2  \\
\end{aligned}
$$

$$
\begin{aligned}
\qquad \qquad & = \frac{1}{\sum \omega_i} \nabla\_{x_t} \sum_i^N \omega_i \|x_t-y_i \|_2^2
\end{aligned}
$$

This gradient formulation is quite similar (up to the weighting) to UniGuide's special case $S=Z$, as it computes an L2 loss on a given conformation ($\{y_i\}$) and does not generalise to arbitrary geometric conditions. In practice, this means that [1] calculates gradients with respect to the surface-defining points of the noisy, generated ligand rather than the condition surface. 

We consider this suboptimal and have experienced that this formulation can lead to instabilities, as it heavily depends on the quality of the noisy samples and never explicitly defines the surface. (Note that we also had similar issues when guiding the clean data point's conformation $\hat{x}_t$ instead of $x_t$.)


Within UniGuide, in contrast, the surface is explicitly defined, and the gradient updates relate directly to the surface. UniGuide's condition map provides guidance targets $c = C(s, \hat{x}_t)$ (see Eq. 20 and 21, manuscript) that are directly associated with the surface, either on the surface or projections into it. For these target conditions $c$, we compute $\nabla\_{x_t} \| \hat{x}_t - c \|_2^2$. This technical difference comes with several advantages:
- The separation of the condition from the generated configuration, combined with the subsequent comparison via a direct L2 loss, shifts the focus to appropriately defining the condition.
- UniGuide does not require the condition definition to be differentiable, offering greater flexibility.
- The condition's explicit nature and the more flexible gradient definition enable us to derive various projections, such as setting a margin for projecting into the surface. This precision is challenging to achieve with a distance-based gradient formulation.

Finally, we would like to reemphasise that UniGuide's formulation is versatile and extends to other tasks, including density-based drug discovery (as noted in our response to D4nw). In contrast, validity guidance shares limitations similar to UniGuide's special case where $S = Z$. We hope this explanation provides a clear and satisfactory understanding of the distinction between how UniGuide implements conditions compared to validity guidance.
    
[1] DECOMPDIFF: Diffusion Models with Decomposed Priors
for Structure-Based Drug Design
I carefully check the rebuttal. 

I am now convinced that Uniguide holds a difference with the direct application of gradient-guided generation and I also appreciate the novelty of geometric condition maps. 

I increased my scores to appreciate the efforts.
Thank you for the follow-up clarification. I have seen the new experiments about comparing UniGuide and validity guidance. However, I'm curious about what the specific difference is in terms of implementing these two methods? From my understanding, they both use the loss in the coordinate space derived from the geometric constraint to guide the diffusion sampling process.
&nbsp;

Thank you for your kind answer and for increasing the score. We are glad that our clarifications and additional results have addressed most of the reviewer's concerns. Below, we would like to offer further clarifications on UniGuide's superiority and distinct advantages over alternative guidance methods that control generation during inference:

&nbsp;

> Highlight the difference to other controlling techniques

- **UniGuide maps the condition to the configuration space**:
  - Prior works [1,2,3], centred around classifier-guidance [1],  guide towards conditions that describe global input properties. For example, [2,3] control the generation of molecules given a desired quantum property. We highlight that such prior works are limited in their applications and cannot (directly) condition on geometric conditions as introduced in our work.  
  - [1,2,3] control the generation during inference usually by mapping the output of the diffusion model to the condition's space $(Z \to S)$, by using a classifier/regressor $f_{\theta}(z_t)$. In other words, the distribution $p_{\theta}(c |z_t)$ takes the form $p_{\theta}(c|z_t) =  \mathcal{N}(c |f_{\theta}(z_t), I).$ In contrast, UniGuide maps the source condition to the configuration space $(S \to Z)$ which simplifies the gradient signal computation  $\nabla_{z_t} p_{\theta}(c |z_t)$ to a squared error between the sample $z_t$ and the target condition $c = C({s}, \hat{z}_t)$ and eliminates the need for additional networks, see Eq.15.
- **UniGuide is a self-guiding method**: UniGuide modifies the reverse process of the unconditional diffusion model without relying on additional networks to guide the generation, unlike [1,2,3] that use additional differentiable networks for guidance. This highlights the flexibility of UniGuide as it does not require additional training: neither training a specialised conditional diffusion model nor training additional classifiers/regressors for guidance.
- **UniGuide is a gradient-based method**: In our experimental evaluations, we include other controlling techniques during inference, such as inpainting or position guidance.
  - For SBDD, inpainting directly inpaints the noised condition to the generation, leading to a perturbed denoising process through the used hard constraints.
  - For LBDD, ShapeMol+g directly leverages the positions of the reference ligands and adds additional position corrections to the conformations based on distance measures. 

&nbsp;

> Elaborate on the superiority of UniGuide

- **Unification** through the condition map: UniGuide leverages a novel condition map to incorporate diverse geometric conditions, such as protein structures, molecular fragments, and molecular surfaces. This extends unconditional base models to diverse drug discovery tasks. Beyond established drug discovery tasks, UniGuide enables tackling entirely novel tasks where neither baselines nor sufficient data exists, e.g. the tasks of density-based drug design or symmetric proteins. We kindly refer the reviewer to the general response and the figures of the PDF.
- **Equivariance**: Different from the text and image domains, equivariance is an important inductive bias of molecular generative modelling. In Theorem 4.1, we derive the conditions on UniGuide's condition map that enable guidance while respecting the molecular domain by maintaining equivariant updates.
- Empirically, our results show that through UniGuide's soft gradient-based updates, we achieve state-of-the-art performance by providing the best trade-off between how well we incorporate the condition into the generative process (LBDD: shape similarity and graph similarity,  SBDD:  Vina) and the overall quality of the molecules (QED, SA, validity). We kindly point the reviewer to Tables 2 & 3 in the PDF.
- Finally, we believe our follow-up response shows UniGuide's superiority over validity guidance. However, we are unsure if the reviewer has seen it. We provide results demonstrating that our condition map is more reliable and outperforms validity guidance regarding shape similarity, highlighting its effectiveness.

&nbsp;

In summary, like classifier guidance, UniGuide controls the generation without additional training. In addition, UniGuide extends this approach [1] to the molecular domain by mapping the source condition to the configuration space. This enables direct self-guidance without additional networks while preserving equivariance. Our experimental evaluations show that UniGuide outperforms various baselines, including other techniques that control the generation solely during inference across multiple downstream tasks. We are thankful for the reviewer’s feedback and hope that our answers sufficiently clarify the remaining concern.

&nbsp;

[1] Dhariwal et al. Diffusion models beat gans on image synthesis

[2] Equivariant Energy-Guided SDE for Inverse Molecular Design

[3] Training-free Multi-objective Diffusion Model for 3D Molecule Generation
Thank you very much for the kind words and for increasing the score of our paper. We are pleased to hear that we were able to resolve the reviewer's concerns.

Best regards,

The Authors
&nbsp;

Thank you for your response and for recognising the additional results we provided as part of our rebuttal. We are glad that our explanations have enhanced the clarity of our paper. Regarding the mention of marginal performance improvements, we have addressed this in detail in our response to YA7u, offering a broader perspective on UniGuide's potential impact and objectives. We kindly refer you to that response and hope it provides further clarity. Specifically for the FBDD experiments, while we agree that Table 2 shows UniGuide's on-par performance with a task-specific model, we would like to emphasise the significantly improved VINA scores by 0.5, as demonstrated in Table 13 of the manuscript. 

&nbsp;

We hope these clarifications highlight UniGuide's full potential. Thank you once again for your valuable feedback and the engaging discussion.
Thank you very much for your response. While we consider UniGuide's performance improvements significant (details below), we want to emphasise that a performance-focused discussion overlooks UniGuide's **broader potential and impact: UniGuide's formulation enables to tackle entirely novel drug discovery tasks where no established baselines or sufficient data exists.** Specifically, our goal is not to adapt existing models to boost their performance in downstream tasks but to provide a generally applicable guidance framework that makes (unconditional) base models useful for various tasks and practical applications.

This capability is well demonstrated in our experiments on density-based drug design (no data) and symmetric proteins (limited base model); see Figures in PDF. Our results show that UniGuide is versatile (EDM was applied to both LBDD & FBDD) and effective, consistently delivering performance that matches or exceeds task-specific models (which are limited to a single task and require extra training) and outperforms alternative conditioning mechanisms.

This sets the basis for UniGuide's long-term objective to reliably translate novel tasks directly to a generative model by incorporating any newly developed geometric conditions through its condition map, thereby accelerating the overall drug discovery process (for real-world applications).

We also want to highlight a selection of our results that demonstrate the consistency and significance of our improvements, and we kindly ask the reviewer to reassess their evaluation in light of this evidence:

- **LBDD**: **UniGuide is state-of-the-art** and outperforms alternative guidance mechanisms (cf. follow-up to our general response). An improvement over the base EDM model for LBDD (as indicated by the reviewer) is not possible as **EDM can only be applied for the LBDD tasks with UniGuide** (Table 3, Rebuttal PDF). 
- **SBDD**: **UniGuide demonstrates superior performance over all evaluated conditioning mechanisms for diffusion models** (cf. follow-up to our general response). Specifically, we improve the base model DiffSBDD in terms VINA score of up to 1 when utilising UniGuide and up to 1.8 when additionally using UniGuide's version of Clash Drift. This results in competitive performance of the base model compared to conditional, task-specific models such as DecompDiff and IPDiff.
- **FBDD**: **UniGuide enhances the VINA score by 0.5 compared to the evaluated baseline for general, pocket-conditioned FBDD tasks** and generates more valid and connected ligands (as shown in Table 13 of the manuscript).

While the observed improvement initially appeared marginal to the reviewer, we believe further consideration of the experimental evidence and UniGuide's potential for novel applications and model enhancement may offer a different perspective. We appreciate your feedback and hope our explanation has been helpful in clarifying UniGuide's potential impact.
Thank the authors for the detailed response! Most of my concerns have been addressed and I'd love to raise my score to 5. However, the authors still didn't show the superiority and highlight the difference of their method compared to some other techniques like classifier guidance, which doesn't need additional training, can also be applied in different application scenarios, and have very similar mathematical formation. That's the main reason for not giving a higher score.
Thank you for the detailed response and improving the clarity of understanding the method.  I believe that the rebuttal adds clarity to the paper. I appreciate the additional results in generating symmetric proteins. However, as other reviewers mentioned, the geometric guidance led to marginal improvements in performance. Further, the additional experiments on rebuttal Table 2 only demonstrate minimal performance improvements. As a result, I maintain my score.
Thank you for the response. Given the additional results and comparison with more diffusion baselines, I'm still a bit concerned about the effectiveness and necessity of introducing geometric guidance, since it only marginally improves upon the performance of backbone models (EDM, DiffSBDD, etc). The author mentioned that these models have not been specifically engineered for certain tasks, but it seems to me that the point of adapting existing models for downstream tasks is primarily aimed to benefit from them so as to boost the task-specific performance, which UniGuide has yet to achieve. In this regard, I'm inclined to maintain the score.
Dear ZcJd, 

As promised in our initial response, we conducted additional experiments to compare UniGuide with an adaption of validity guidance for LBDD and included a version of "clash drift" into UniGuide's condition map for SBDD. As we believe that the results are relevant to all reviewers, we kindly refer you to our official comment. Thank you again for your valuable feedback.

&nbsp;

Best regards, 

The Authors
### Follow-Up on Comparison of UniGuide with validity guidance

&nbsp;

We want to follow up on the “Validity Guidance” discussion (ZcJd), as mentioned in [1]. **We have conducted experiments using the surface loss computation and self-guidance for the LBDD task.** We selected the hyperparameters $\sigma$ and $\gamma$ in the surface loss computation to achieve a high DICE score between the implicitly defined surface ($S=\gamma$) and the meshes UniGuide utilises for LBDD ($\sigma=1$,  $\gamma=2$, DICE > 0.8). Our surface calculations are performed using the Open Drug Discovery Toolkit (ODDT), which assigns specific radii to individual atom types and employs the marching cubes algorithm to generate meshes [2].

We performed several runs around the above hyperparameter specifications. The runs were similar in performance and we report the best result below: 

| |$\text{Sim}_S ~(\uparrow)$ | $\text{maxSim}_S~~(\uparrow)$ | $\text{Sim}_G ~(\downarrow)$ | $\text{maxSim}_G ~(\downarrow)$ | **Ratio** $(\uparrow)$ |  Connect. $(\uparrow)$ | Unique. $(\uparrow)$ | Diversity $(\uparrow)$ | QED $(\uparrow)$ |
| -------- | -------- | -------- | -------- | -------- | -------- | -------- | -------- | -------- | -------- |
| Validity Guidance     | 0.59     | 0.76 | 0.20 | 0.20 | **2.96** | 97%| 100% | 0.76 | 0.69 |
| UniGuide (EDM) | 0.74 | 0.86 | 0.21 | 0.20 | **3.53** | 99%| 99% | 0.73 | 0.74 |


**Although Validity Guidance for LBDD yields low graph similarity, the shape similarity remains suboptimal compared to UniGuide.** Additionally, we frequently encounter numerical instability for this guidance term, an issue not present with UniGuide’s formulation of LBDD.

We believe this ablation will provide a valuable comparison for the final version of our manuscript and hope we have addressed the reviewer's remaining concerns.

&nbsp;

[1] 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.

[2] Lorensen, William E., and Harvey E. Cline. Marching cubes: A high resolution 3D surface construction algorithm, 1998

&nbsp;
&nbsp;

### Follow-Up on SBDD

&nbsp;

We want to follow up on the discussion regarding baselines for SBDD (ZcJd & YA7u), specifically IPDiff [1] and DecompDiff [2]. As previously mentioned, incorporating a form of "Clash Drift" into UniGuide, particularly within the condition map, is straightforward and helps prevent the generated ligand from colliding with the pocket. **We have implemented this adjustment, and our initial results indicate that similar to IPDiff and DecompDiff, it improves the overall VINA scores.** Specifically, UniGuide's VINA score, compared to the results reported in Table 1 of the rebuttal PDF, **improved significantly from −5.074 to -5.81. These initial results are promising and we are confident that adjustments of UniGuide's guidance parameters will lead to further improvments.**

We again appreciate the reviewers' suggestions to include [1, 2] and believe that these additional results underscore UniGuide's flexibility to readily incorporate various conditions, enabling the comparison of underlying models across different levels. We hope that these findings address all the reviewers' remaining concerns, and we are looking forward to discussing these additional results.

&nbsp;

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

[2] Guan et al. DecompDiff: diffusion models with decomposed priors for SBDD
Thanks for your explanations and additional results. My concern has been resolved and I have raised my score to 7.