Accurate thermochemical data with sub-chemical accuracy (within 1 kcal mol-1 of the empirical ground truth) are essential for advancing computational chemistry methods. However, existing datasets that reach this level of accuracy remain limited in size or scope. This hinders the development of data-driven methods with predictive accuracy across the broad chemical space of closed-shell, neutral molecules. Here we present Microsoft Research Accurate Chemistry Collection (MSR-ACC) and its first release, MSR-ACC/TAE25, comprising 73,040 total atomization energies at the CCSD(T)/CBS level obtained with the W1-F12 thermochemical protocol. The dataset is constructed to exhaustively cover the chemical space of closed-shell, charge-neutral, covalently bound equilibrium molecular structures containing up to 5 non-hydrogen atoms drawn from elements up to argon and lacking significant multireference character. The dataset and its canonical train and validation splits are openly available on Zenodo in the QCSchema format under the CDLA Permissive 2.0 license. This first release of MSR-ACC enables data-driven approaches for developing predictive computational chemistry methods with unprecedented accuracy and scope.

Following the sequence and structure revolutions, predicting functionally relevant protein structure changes at scale remains an outstanding challenge. We introduce BioEmu, a deep learning system that emulates protein equilibrium ensembles by generating thousands of statistically independent structures per hour on a single graphics processing unit (GPU). BioEmu integrates more than 200 milliseconds of molecular dynamics (MD) simulations, static structures, and experimental protein stabilities using new training algorithms. It captures diverse functional motions-including cryptic pocket formation, local unfolding, and domain rearrangements-and predicts relative free energies with 1 kilocalorie per mole accuracy compared with millisecond-scale MD and experimental data. BioEmu provides mechanistic insights by jointly modeling structural ensembles and thermodynamic properties. This approach amortizes the cost of MD and experimental data generation, demonstrating a scalable path toward understanding and designing protein function.

Solving computer-aided synthesis planning is essential for enabling fully automated, robot-assisted synthesis workflows and improving the efficiency of drug discovery. A key challenge, however, is bridging the gap between computational route design and practical laboratory execution, particularly the accurate prediction of viable experimental procedures for each synthesis step. In this work, we present QFANG, a scientific reasoning language model capable of generating precise, structured experimental procedures directly from reaction equations, with explicit chain-of-thought reasoning. To develop QFANG, we curated a high-quality dataset comprising 905,990 chemical reactions paired with structured action sequences, extracted and processed from patent literature using large language models. We introduce a Chemistry-Guided Reasoning (CGR) framework that produces chain-of-thought data grounded in chemical knowledge at scale. The model subsequently undergoes supervised fine-tuning to elicit complex chemistry reasoning. Finally, we apply Reinforcement Learning from Verifiable Rewards (RLVR) to further enhance procedural accuracy. Experimental results demonstrate that QFANG outperforms advanced general-purpose reasoning models and nearest-neighbor retrieval baselines, measured by traditional NLP similarity metrics and a chemically aware evaluator using an LLM-as-a-judge. Moreover, QFANG generalizes to certain out-of-domain reaction classes and adapts to variations in laboratory conditions and user-specific constraints. We believe that QFANG's ability to generate high-quality synthesis procedures represents an important step toward bridging the gap between computational synthesis planning and fully automated laboratory synthesis.

Protein design often begins with the knowledge of a desired function from a motif which motif-scaffolding aims to construct a functional protein around. Recently, generative models have achieved breakthrough success in designing scaffolds for a range of motifs. However, generated scaffolds tend to lack structural diversity, which can hinder success in wet-lab validation. In this work, we extend FrameFlow, an SE(3) flow matching model for protein backbone generation, to perform motif-scaffolding with two complementary approaches. The first is motif amortization, in which FrameFlow is trained with the motif as input using a data augmentation strategy. The second is motif guidance, which performs scaffolding using an estimate of the conditional score from FrameFlow without additional training. On a benchmark of 24 biologically meaningful motifs, we show our method achieves 2.5 times more designable and unique motif-scaffolds compared to state-of-the-art. Code: https://github.com/microsoft/protein-frame-flow

Fragment-based drug discovery has been an effective paradigm in early-stage drug development. An open challenge in this area is designing linkers between disconnected molecular fragments of interest to obtain chemically-relevant candidate drug molecules. In this work, we propose DiffLinker, an E(3)-equivariant 3D-conditional diffusion model for molecular linker design. Given a set of disconnected fragments, our model places missing atoms in between and designs a molecule incorporating all the initial fragments. Unlike previous approaches that are only able to connect pairs of molecular fragments, our method can link an arbitrary number of fragments. Additionally, the model automatically determines the number of atoms in the linker and its attachment points to the input fragments. We demonstrate that DiffLinker outperforms other methods on the standard datasets generating more diverse and synthetically-accessible molecules. Besides, we experimentally test our method in real-world applications, showing that it can successfully generate valid linkers conditioned on target protein pockets.

Coarse-grained (CG) molecular dynamics enables the study of biological processes at temporal and spatial scales that would be intractable at an atomistic resolution. However, accurately learning a CG force field remains a challenge. In this work, we leverage connections between score-based generative models, force fields, and molecular dynamics to learn a CG force field without requiring any force inputs during training. Specifically, we train a diffusion generative model on protein structures from molecular dynamics simulations, and we show that its score function approximates a force field that can directly be used to simulate CG molecular dynamics. While having a vastly simplified training setup compared to previous work, we demonstrate that our approach leads to improved performance across several protein simulations for systems up to 56 amino acids, reproducing the CG equilibrium distribution and preserving the dynamics of all-atom simulations such as protein folding events.

We present FrameFlow, a method for fast protein backbone generation using SE(3) flow matching. Specifically, we adapt FrameDiff, a state-of-the-art diffusion model, to the flow-matching generative modeling paradigm. We show how flow matching can be applied on SE(3) and propose modifications during training to effectively learn the vector field. Compared to FrameDiff, FrameFlow requires five times fewer sampling timesteps while achieving two fold better designability. The ability to generate high quality protein samples at a fraction of the cost of previous methods paves the way towards more efficient generative models in de novo protein design.

This work introduces a diffusion model for molecule generation in 3D that is equivariant to Euclidean transformations. Our E(3) Equivariant Diffusion Model (EDM) learns to denoise a diffusion process with an equivariant network that jointly operates on both continuous (atom coordinates) and categorical features (atom types). In addition, we provide a probabilistic analysis which admits likelihood computation of molecules using our model. Experimentally, the proposed method significantly outperforms previous 3D molecular generative methods regarding the quality of generated samples and efficiency at training time.

This paper introduces a new architecture for multivariate time series forecasting that simultaneously infers and leverages relations among time series. We cast our method as a modular extension to univariate architectures where relations among individual time series are dynamically inferred in the latent space obtained after encoding the whole input signal. Our approach is flexible enough to scale gracefully according to the needs of the forecasting task under consideration. In its most straight-forward and general version, we infer a potentially fully connected graph to model the interactions between time series, which allows us to obtain competitive forecast accuracy compared with the state-of-the-art in graph neural networks for forecasting. In addition, whereas previous latent graph inference methods scale O(N^2) w.r.t. the number of nodes N (representing the time series), we show how to configure our approach to cater for the scale of modern time series panels. By assuming the inferred graph to be bipartite where one partition consists of the original N nodes and we introduce K nodes (taking inspiration from low-rank-decompositions) we reduce the time complexity of our procedure to O(NK). This allows us to leverage the dependency structure with a small trade-off in forecasting accuracy. We demonstrate the effectiveness of our method for a variety of datasets where it performs better or very competitively to previous methods under both the fully connected and bipartite assumptions.

This paper introduces a new approach for Multivariate Time Series forecasting that jointly infers and leverages relations among time series. Its modularity allows it to be integrated with current univariate methods. Our approach allows to trade-off accuracy and computational efficiency gradually via offering on one extreme inference of a potentially fully-connected graph or on another extreme a bipartite graph. In the potentially fully-connected case we consider all pair-wise interactions among time-series which yields the best forecasting accuracy. Conversely, the bipartite case leverages the dependency structure by inter-communicating the N time series through a small set of K auxiliary nodes that we introduce. This reduces the time and memory complexity w.r.t. previous graph inference methods from O(N^2) to O(NK) with a small trade-off in accuracy. We demonstrate the effectiveness of our model in a variety of datasets where both of its variants perform better or very competitively to previous graph inference methods in terms of forecasting accuracy and time efficiency.

This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does not require computationally expensive higher-order representations in intermediate layers while it still achieves competitive or better performance. In addition, whereas existing methods are limited to equivariance on 3 dimensional spaces, our model is easily scaled to higher-dimensional spaces. We demonstrate the effectiveness of our method on dynamical systems modelling, representation learning in graph autoencoders and predicting molecular properties.

This paper introduces a generative model equivariant to Euclidean symmetries: E(n) Equivariant Normalizing Flows (E-NFs). To construct E-NFs, we take the discriminative E(n) graph neural networks and integrate them as a differential equation to obtain an invertible equivariant function: a continuous-time normalizing flow. We demonstrate that E-NFs considerably outperform baselines and existing methods from the literature on particle systems such as DW4 and LJ13, and on molecules from QM9 in terms of log-likelihood. To the best of our knowledge, this is the first flow that jointly generates molecule features and positions in 3D.

A graphical model is a structured representation of locally dependent random variables. A traditional method to reason over these random variables is to perform inference using belief propagation. When provided with the true data generating process, belief propagation can infer the optimal posterior probability estimates in tree structured factor graphs. However, in many cases we may only have access to a poor approximation of the data generating process, or we may face loops in the factor graph, leading to suboptimal estimates. In this work we first extend graph neural networks to factor graphs (FG-GNN). We then propose a new hybrid model that runs conjointly a FG-GNN with belief propagation. The FG-GNN receives as input messages from belief propagation at every inference iteration and outputs a corrected version of them. As a result, we obtain a more accurate algorithm that combines the benefits of both belief propagation and graph neural networks. We apply our ideas to error correction decoding tasks, and we show that our algorithm can outperform belief propagation for LDPC codes on bursty channels.

We study a recent class of models which uses graph neural networks (GNNs) to improve forecasting in multivariate time series. The core assumption behind these models is that there is a latent graph between the time series (nodes) that governs the evolution of the multivariate time series. By parameterizing a graph in a differentiable way, the models aim to improve forecasting quality. We compare four recent models of this class on the forecasting task. Further, we perform ablations to study their behavior under changing conditions, e.g., when disabling the graph-learning modules and providing the ground-truth relations instead. Based on our findings, we propose novel ways of combining the existing architectures.

This paper introduces a generative model equivariant to Euclidean symmetries: E(n) Equivariant Normalizing Flows (E-NFs). To construct E-NFs, we take the discriminative E(n) graph neural networks and integrate them as a differential equation to obtain an invertible equivariant function: a continuous-time normalizing flow. We demonstrate that E-NFs considerably outperform baselines and existing methods from the literature on particle systems such as DW4 and LJ13, and on molecules from QM9 in terms of log-likelihood. To the best of our knowledge, this is the first likelihood-based deep generative model that generates molecules in 3D.

Proof. Let W = Q and let fAR(x) = R̃h(Rx+ b). Indeed, any orthogonal matrix is invertible, so Q can be modelled by W. Also, note that R and R̃ are upper triangular and h is an elementwise function. The matrix product of the Jacobians is triangular, and thus R̃h(Rx+ b) has a triangular Jacobian and is therefore autoregressive. Hence, it can be modelled by fAR. Further, note that [10] bound RiiR̃ii > −1 ||h′||∞ , which ensures that the constraint ∂fAR(x)i ∂xi > −1 is satisfied. Hence, z = x +Q R̃h(RQx + b) can be written as Equation 1 when writing fAR(x) = R̃h(Rx + b) and M = Q without violating any constraints on M and fAR, and is therefore a special case. Remark 1: The increased expressitivity originates from fAR and not from W. To see why, suppose we replace Q and Q in the original formulation by W and W−1. Consider that any real square matrix W may be decomposed as QWRW. Hence, compositions W−1R̃ and RW can be written as QWR̃ ′ and RQW, where R̃′ = R−1 W R̃ and R ′ = RRW which are both still upper triangular. Hence, we have shown that even if the orthogonal matrix Q is replaced by an invertible matrix W, the transformation can still be written in terms of a shared orthogonal matrix QW and upper triangular matrices R̃′ and R′. Therefore, the source of the increased expressitivity is not the replacement of Q by W.

This paper introduces a new method to build linear flows, by taking the exponential of a linear transformation. This linear transformation does not need to be invertible itself, and the exponential has the following desirable properties: it is guaranteed to be invertible, its inverse is straightforward to compute and the log Jacobian determinant is equal to the trace of the linear transformation. An important insight is that the exponential can be computed implicitly, which allows the use of convolutional layers. Using this insight, we develop new invertible transformations named convolution exponentials and graph convolution exponentials , which retain the equivariance of their underlying transformations. Empirically, we show that the convolution exponential outperforms other linear transformations in generative flows on CIFAR10 and the graph convolution exponential improves the performance of graph normalizing flows.

This paper introduces a new method to build linear flows, by taking the exponential of a linear transformation. This linear transformation does not need to be invertible itself, and the exponential has the following desirable properties: it is guaranteed to be invertible, its inverse is straightforward to compute and the log Jacobian determinant is equal to the trace of the linear transformation. An important insight is that the exponential can be computed implicitly, which allows the use of convolutional layers. Using this insight, we develop new invertible transformations named convolution exponentials and graph convolution exponentials, which retain the equivariance of their underlying transformations. In addition, we generalize Sylvester Flows and propose Convolutional Sylvester Flows which are based on the generalization and the convolution exponential as basis change. Empirically, we show that the convolution exponential outperforms other linear transformations in generative flows on CIFAR10 and the graph convolution exponential improves the performance of graph normalizing flows. In addition, we show that Convolutional Sylvester Flows improve performance over residual flows as a generative flow model measured in log-likelihood.

A graphical model is a structured representation of the data generating process. The traditional method to reason over random variables is to perform inference in this graphical model. However, in many cases the generating process is only a poor approximation of the much more complex true data generating process, leading to suboptimal estimation. The subtleties of the generative process are however captured in the data itself and we can `learn to infer', that is, learn a direct mapping from observations to explanatory latent variables. In this work we propose a hybrid model that combines graphical inference with a learned inverse model, which we structure as in a graph neural network, while the iterative algorithm as a whole is formulated as a recurrent neural network. By using cross-validation we can automatically balance the amount of work performed by graphical inference versus learned inference. We apply our ideas to the Kalman filter, a Gaussian hidden Markov model for time sequences, and show, among other things, that our model can estimate the trajectory of a noisy chaotic Lorenz Attractor much more accurately than either the learned or graphical inference run in isolation.

We propose to study the problem of few-shot learning with the prism of inference on a partially observed graphical model, constructed from a collection of input images whose label can be either observed or not. By assimilating generic message-passing inference algorithms with their neural-network counterparts, we define a graph neural network architecture that generalizes several of the recently proposed few-shot learning models. Besides providing improved numerical performance, our framework is easily extended to variants of few-shot learning, such as semi-supervised or active learning, demonstrating the ability of graph-based models to operate well on 'relational' tasks.