Jarrid Rector-Brooks

Alexander Tong, Kilian Fatras, Nikolay Malkin et al. · mila

Continuous normalizing flows (CNFs) are an attractive generative modeling technique, but they have been held back by limitations in their simulation-based maximum likelihood training. We introduce the generalized conditional flow matching (CFM) technique, a family of simulation-free training objectives for CNFs. CFM features a stable regression objective like that used to train the stochastic flow in diffusion models but enjoys the efficient inference of deterministic flow models. In contrast to both diffusion models and prior CNF training algorithms, CFM does not require the source distribution to be Gaussian or require evaluation of its density. A variant of our objective is optimal transport CFM (OT-CFM), which creates simpler flows that are more stable to train and lead to faster inference, as evaluated in our experiments. Furthermore, we show that when the true OT plan is available, our OT-CFM method approximates dynamic OT. Training CNFs with CFM improves results on a variety of conditional and unconditional generation tasks, such as inferring single cell dynamics, unsupervised image translation, and Schrödinger bridge inference.

Moksh Jain, Emmanuel Bengio, Alex-Hernandez Garcia et al. · mila

Design of de novo biological sequences with desired properties, like protein and DNA sequences, often involves an active loop with several rounds of molecule ideation and expensive wet-lab evaluations. These experiments can consist of multiple stages, with increasing levels of precision and cost of evaluation, where candidates are filtered. This makes the diversity of proposed candidates a key consideration in the ideation phase. In this work, we propose an active learning algorithm leveraging epistemic uncertainty estimation and the recently proposed GFlowNets as a generator of diverse candidate solutions, with the objective to obtain a diverse batch of useful (as defined by some utility function, for example, the predicted anti-microbial activity of a peptide) and informative candidates after each round. We also propose a scheme to incorporate existing labeled datasets of candidates, in addition to a reward function, to speed up learning in GFlowNets. We present empirical results on several biological sequence design tasks, and we find that our method generates more diverse and novel batches with high scoring candidates compared to existing approaches.

Kanika Madan, Jarrid Rector-Brooks, Maksym Korablyov et al. · mila

Generative flow networks (GFlowNets) are a family of algorithms for training a sequential sampler of discrete objects under an unnormalized target density and have been successfully used for various probabilistic modeling tasks. Existing training objectives for GFlowNets are either local to states or transitions, or propagate a reward signal over an entire sampling trajectory. We argue that these alternatives represent opposite ends of a gradient bias-variance tradeoff and propose a way to exploit this tradeoff to mitigate its harmful effects. Inspired by the TD($λ$) algorithm in reinforcement learning, we introduce subtrajectory balance or SubTB($λ$), a GFlowNet training objective that can learn from partial action subsequences of varying lengths. We show that SubTB($λ$) accelerates sampler convergence in previously studied and new environments and enables training GFlowNets in environments with longer action sequences and sparser reward landscapes than what was possible before. We also perform a comparative analysis of stochastic gradient dynamics, shedding light on the bias-variance tradeoff in GFlowNet training and the advantages of subtrajectory balance.

Moksh Jain, Sharath Chandra Raparthy, Alex Hernandez-Garcia et al. · mila

We study the problem of generating diverse candidates in the context of Multi-Objective Optimization. In many applications of machine learning such as drug discovery and material design, the goal is to generate candidates which simultaneously optimize a set of potentially conflicting objectives. Moreover, these objectives are often imperfect evaluations of some underlying property of interest, making it important to generate diverse candidates to have multiple options for expensive downstream evaluations. We propose Multi-Objective GFlowNets (MOGFNs), a novel method for generating diverse Pareto optimal solutions, based on GFlowNets. We introduce two variants of MOGFNs: MOGFN-PC, which models a family of independent sub-problems defined by a scalarization function, with reward-conditional GFlowNets, and MOGFN-AL, which solves a sequence of sub-problems defined by an acquisition function in an active learning loop. Our experiments on wide variety of synthetic and benchmark tasks demonstrate advantages of the proposed methods in terms of the Pareto performance and importantly, improved candidate diversity, which is the main contribution of this work.

Jarrid Rector-Brooks, Kanika Madan, Moksh Jain et al. · mila

Generative flow networks (GFlowNets) are amortized variational inference algorithms that treat sampling from a distribution over compositional objects as a sequential decision-making problem with a learnable action policy. Unlike other algorithms for hierarchical sampling that optimize a variational bound, GFlowNet algorithms can stably run off-policy, which can be advantageous for discovering modes of the target distribution. Despite this flexibility in the choice of behaviour policy, the optimal way of efficiently selecting trajectories for training has not yet been systematically explored. In this paper, we view the choice of trajectories for training as an active learning problem and approach it using Bayesian techniques inspired by methods for multi-armed bandits. The proposed algorithm, Thompson sampling GFlowNets (TS-GFN), maintains an approximate posterior distribution over policies and samples trajectories from this posterior for training. We show in two domains that TS-GFN yields improved exploration and thus faster convergence to the target distribution than the off-policy exploration strategies used in past work.

Jarrid Rector-Brooks, Théophile Lambert, Marta Skreta et al.

Evolution is an extraordinary engine for enzymatic diversity, yet the chemistry it has explored remains a narrow slice of what DNA can encode. Deep generative models can design new proteins that bind ligands, but none have created enzymes without pre-specifying catalytic residues. We introduce DISCO (DIffusion for Sequence-structure CO-design), a multimodal model that co-designs protein sequence and 3D structure around arbitrary biomolecules, as well as inference-time scaling methods that optimize objectives across both modalities. Conditioned solely on reactive intermediates, DISCO designs diverse heme enzymes with novel active-site geometries. These enzymes catalyze new-to-nature carbene-transfer reactions, including alkene cyclopropanation, spirocyclopropanation, B-H, and C(sp$^3$)-H insertions, with high activities exceeding those of engineered enzymes. Random mutagenesis of a selected design further confirmed that enzyme activity can be improved through directed evolution. By providing a scalable route to evolvable enzymes, DISCO broadens the potential scope of genetically encodable transformations. Code is available at https://github.com/DISCO-design/DISCO.

Avishek Joey Bose, Tara Akhound-Sadegh, Guillaume Huguet et al.

The computational design of novel protein structures has the potential to impact numerous scientific disciplines greatly. Toward this goal, we introduce FoldFlow, a series of novel generative models of increasing modeling power based on the flow-matching paradigm over $3\mathrm{D}$ rigid motions -- i.e. the group $\text{SE}(3)$ -- enabling accurate modeling of protein backbones. We first introduce FoldFlow-Base, a simulation-free approach to learning deterministic continuous-time dynamics and matching invariant target distributions on $\text{SE}(3)$. We next accelerate training by incorporating Riemannian optimal transport to create FoldFlow-OT, leading to the construction of both more simple and stable flows. Finally, we design FoldFlow-SFM, coupling both Riemannian OT and simulation-free training to learn stochastic continuous-time dynamics over $\text{SE}(3)$. Our family of FoldFlow, generative models offers several key advantages over previous approaches to the generative modeling of proteins: they are more stable and faster to train than diffusion-based approaches, and our models enjoy the ability to map any invariant source distribution to any invariant target distribution over $\text{SE}(3)$. Empirically, we validate FoldFlow, on protein backbone generation of up to $300$ amino acids leading to high-quality designable, diverse, and novel samples.

Marcin Sendera, Minsu Kim, Sarthak Mittal et al.

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods (continuous generative flow networks). Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work. We also propose a novel exploration strategy for off-policy methods, based on local search in the target space with the use of a replay buffer, and show that it improves the quality of samples on a variety of target distributions. Our code for the sampling methods and benchmarks studied is made public at https://github.com/GFNOrg/gfn-diffusion as a base for future work on diffusion models for amortized inference.

Emily Jin, Andrei Cristian Nica, Mikhail Galkin et al.

Accurately predicting experimentally-realizable 3D molecular crystal structures from their 2D chemical graphs is a long-standing open challenge in computational chemistry called crystal structure prediction (CSP). Efficiently solving this problem has implications ranging from pharmaceuticals to organic semiconductors, as crystal packing directly governs the physical and chemical properties of organic solids. In this paper, we introduce OXtal, a large-scale 100M parameter all-atom diffusion model that directly learns the conditional joint distribution over intramolecular conformations and periodic packing. To efficiently scale OXtal, we abandon explicit equivariant architectures imposing inductive bias arising from crystal symmetries in favor of data augmentation strategies. We further propose a novel crystallization-inspired lattice-free training scheme, Stoichiometric Stochastic Shell Sampling ($S^4$), that efficiently captures long-range interactions while sidestepping explicit lattice parametrization -- thus enabling more scalable architectural choices at all-atom resolution. By leveraging a large dataset of 600K experimentally validated crystal structures (including rigid and flexible molecules, co-crystals, and solvates), OXtal achieves orders-of-magnitude improvements over prior ab initio machine learning CSP methods, while remaining orders of magnitude cheaper than traditional quantum-chemical approaches. Specifically, OXtal recovers experimental structures with conformer $\text{RMSD}_1<0.5$ Å and attains over 80\% packing similarity rate, demonstrating its ability to model both thermodynamic and kinetic regularities of molecular crystallization.

Tara Akhound-Sadegh, Jarrid Rector-Brooks, Avishek Joey Bose et al.

Efficiently generating statistically independent samples from an unnormalized probability distribution, such as equilibrium samples of many-body systems, is a foundational problem in science. In this paper, we propose Iterated Denoising Energy Matching (iDEM), an iterative algorithm that uses a novel stochastic score matching objective leveraging solely the energy function and its gradient -- and no data samples -- to train a diffusion-based sampler. Specifically, iDEM alternates between (I) sampling regions of high model density from a diffusion-based sampler and (II) using these samples in our stochastic matching objective to further improve the sampler. iDEM is scalable to high dimensions as the inner matching objective, is simulation-free, and requires no MCMC samples. Moreover, by leveraging the fast mode mixing behavior of diffusion, iDEM smooths out the energy landscape enabling efficient exploration and learning of an amortized sampler. We evaluate iDEM on a suite of tasks ranging from standard synthetic energy functions to invariant $n$-body particle systems. We show that the proposed approach achieves state-of-the-art performance on all metrics and trains $2-5\times$ faster, which allows it to be the first method to train using energy on the challenging $55$-particle Lennard-Jones system.

Fred Zhangzhi Peng, Zachary Bezemek, Sawan Patel et al.

Any order generation of discrete data using masked diffusion models (MDMs) offers a compelling alternative to traditional autoregressive models, especially in domains that lack a natural causal ordering of data. However, current popular MDMs depart from their successful continuous diffusion model counterparts with simplified masked inference wherein unmasked tokens cannot be iteratively refined -- even if there is a mistake. In this paper, we extract the full power of MDMs by introducing a novel inference sampling strategy termed Path Planning (P2) that decomposes each generation step into two sub-stages: planning and denoising. Under P2, the planner at every step selects appropriate tokens that are marked to be updated, which can then be sampled using the denoiser. We demonstrate that P2 generalizes all existing sampling strategies for MDMs and critically enhances generative quality through the new capability of refining and updating existing unmasked tokens. We theoretically prove that P2 establishes a (new) expanded evidence lower bound (ELBO) on the log marginal likelihood of data. We instantiate P2 with a family of planners including: 1.) Self-Planning, 2.) BERT-Planning, and 3.) Trained-Planning with a learned planner leading to SOTA generative performance for MDMs on a suite of domains. Specifically, solely using P2 inference, we observe relative improvements of 22% in protein sequence foldability, 8% in RNA sequence pLDDT, 4% in math reasoning, 68% in story generation (ROUGE score), and 33% in code generation for the challenging pass@1 metric.

Julius Berner, Lorenz Richter, Marcin Sendera et al.

We study the problem of training neural stochastic differential equations, or diffusion models, to sample from a Boltzmann distribution without access to target samples. Existing methods for training such models enforce time-reversal of the generative and noising processes, using either differentiable simulation or off-policy reinforcement learning (RL). We prove equivalences between families of objectives in the limit of infinitesimal discretization steps, linking entropic RL methods (GFlowNets) with continuous-time objects (partial differential equations and path space measures). We further show that an appropriate choice of coarse time discretization during training allows greatly improved sample efficiency and the use of time-local objectives, achieving competitive performance on standard sampling benchmarks with reduced computational cost.

Maksym Korablyov, Cheng-Hao Liu, Moksh Jain et al. · mila

Despite substantial progress in machine learning for scientific discovery in recent years, truly de novo design of small molecules which exhibit a property of interest remains a significant challenge. We introduce LambdaZero, a generative active learning approach to search for synthesizable molecules. Powered by deep reinforcement learning, LambdaZero learns to search over the vast space of molecules to discover candidates with a desired property. We apply LambdaZero with molecular docking to design novel small molecules that inhibit the enzyme soluble Epoxide Hydrolase 2 (sEH), while enforcing constraints on synthesizability and drug-likeliness. LambdaZero provides an exponential speedup in terms of the number of calls to the expensive molecular docking oracle, and LambdaZero de novo designed molecules reach docking scores that would otherwise require the virtual screening of a hundred billion molecules. Importantly, LambdaZero discovers novel scaffolds of synthesizable, drug-like inhibitors for sEH. In in vitro experimental validation, a series of ligands from a generated quinazoline-based scaffold were synthesized, and the lead inhibitor N-(4,6-di(pyrrolidin-1-yl)quinazolin-2-yl)-N-methylbenzamide (UM0152893) displayed sub-micromolar enzyme inhibition of sEH.

Fred Zhangzhi Peng, Zachary Bezemek, Jarrid Rector-Brooks et al.

Diffusion language models have emerged as a powerful alternative to autoregressive models, enabling fast inference through flexible and parallel generation paths. This flexibility is enabled by new sampling strategies, or planners, that iteratively choose where to denoise along the sequence rather than sampling uniformly at random. However, by modifying reverse paths, planners introduce a mismatch between the uniformly random denoising paths used during training and the planning-based paths used at inference. In this work, we systematically investigate this mismatch and theoretically show that the standard discrete diffusion training evidence lower bound (ELBO) does not accurately describe a denoiser under non-uniform planning. To bridge this gap, we derive a new Planned Evidence Lower Bound (P-ELBO) that directly incorporates planner-based reverse dynamics into the training objective. Building on this, we propose Planner Aware Path Learning (PAPL), a simple and effective modification of the standard masked discrete diffusion loss that aligns training and inference under planned denoisers. Empirically, PAPL delivers consistent improvements across domains, including a 40% relative gain in protein sequence modeling, up to a 4x improvement in MAUVE for text generation, and a 23% relative gain in HumanEval pass@10 for code generation.

Luca Scimeca, Siddarth Venkatraman, Moksh Jain et al. · mila

This paper presents a practical application of Relative Trajectory Balance (RTB), a recently introduced off-policy reinforcement learning (RL) objective that can asymptotically solve Bayesian inverse problems optimally. We extend the original work by using RTB to train conditional diffusion model posteriors from pretrained unconditional priors for challenging linear and non-linear inverse problems in vision, and science. We use the objective alongside techniques such as off-policy backtracking exploration to improve training. Importantly, our results show that existing training-free diffusion posterior methods struggle to perform effective posterior inference in latent space due to inherent biases.

Paul Bertin, Jarrid Rector-Brooks, Deepak Sharma et al.

For large libraries of small molecules, exhaustive combinatorial chemical screens become infeasible to perform when considering a range of disease models, assay conditions, and dose ranges. Deep learning models have achieved state of the art results in silico for the prediction of synergy scores. However, databases of drug combinations are biased towards synergistic agents and these results do not necessarily generalise out of distribution. We employ a sequential model optimization search utilising a deep learning model to quickly discover synergistic drug combinations active against a cancer cell line, requiring substantially less screening than an exhaustive evaluation. Our small scale wet lab experiments only account for evaluation of ~5% of the total search space. After only 3 rounds of ML-guided in vitro experimentation (including a calibration round), we find that the set of drug pairs queried is enriched for highly synergistic combinations; two additional rounds of ML-guided experiments were performed to ensure reproducibility of trends. Remarkably, we rediscover drug combinations later confirmed to be under study within clinical trials. Moreover, we find that drug embeddings generated using only structural information begin to reflect mechanisms of action. Prior in silico benchmarking suggests we can enrich search queries by a factor of ~5-10x for highly synergistic drug combinations by using sequential rounds of evaluation when compared to random selection, or by a factor of >3x when using a pretrained model selecting all drug combinations at a single time point.

Salem Lahlou, Moksh Jain, Hadi Nekoei et al.

Epistemic Uncertainty is a measure of the lack of knowledge of a learner which diminishes with more evidence. While existing work focuses on using the variance of the Bayesian posterior due to parameter uncertainty as a measure of epistemic uncertainty, we argue that this does not capture the part of lack of knowledge induced by model misspecification. We discuss how the excess risk, which is the gap between the generalization error of a predictor and the Bayes predictor, is a sound measure of epistemic uncertainty which captures the effect of model misspecification. We thus propose a principled framework for directly estimating the excess risk by learning a secondary predictor for the generalization error and subtracting an estimate of aleatoric uncertainty, i.e., intrinsic unpredictability. We discuss the merits of this novel measure of epistemic uncertainty, and highlight how it differs from variance-based measures of epistemic uncertainty and addresses its major pitfall. Our framework, Direct Epistemic Uncertainty Prediction (DEUP) is particularly interesting in interactive learning environments, where the learner is allowed to acquire novel examples in each round. Through a wide set of experiments, we illustrate how existing methods in sequential model optimization can be improved with epistemic uncertainty estimates from DEUP, and how DEUP can be used to drive exploration in reinforcement learning. We also evaluate the quality of uncertainty estimates from DEUP for probabilistic image classification and predicting synergies of drug combinations.

Jarrid Rector-Brooks, Jun-Kun Wang, Barzan Mozafari

We revisit the Frank-Wolfe (FW) optimization under strongly convex constraint sets. We provide a faster convergence rate for FW without line search, showing that a previously overlooked variant of FW is indeed faster than the standard variant. With line search, we show that FW can converge to the global optimum, even for smooth functions that are not convex, but are quasi-convex and locally-Lipschitz. We also show that, for the general case of (smooth) non-convex functions, FW with line search converges with high probability to a stationary point at a rate of $O\left(\frac{1}{t}\right)$, as long as the constraint set is strongly convex -- one of the fastest convergence rates in non-convex optimization.