Molecular dynamics (MD) simulation techniques are widely used for various natural science applications. Increasingly, machine learning (ML) force field (FF) models begin to replace ab-initio simulations by predicting forces directly from atomic structures. Despite significant progress in this area, such techniques are primarily benchmarked by their force/energy prediction errors, even though the practical use case would be to produce realistic MD trajectories. We aim to fill this gap by introducing a novel benchmark suite for learned MD simulation. We curate representative MD systems, including water, organic molecules, a peptide, and materials, and design evaluation metrics corresponding to the scientific objectives of respective systems. We benchmark a collection of state-of-the-art (SOTA) ML FF models and illustrate, in particular, how the commonly benchmarked force accuracy is not well aligned with relevant simulation metrics. We demonstrate when and how selected SOTA methods fail, along with offering directions for further improvement. Specifically, we identify stability as a key metric for ML models to improve. Our benchmark suite comes with a comprehensive open-source codebase for training and simulation with ML FFs to facilitate future work.
We propose a new "Poisson flow" generative model (PFGM) that maps a uniform distribution on a high-dimensional hemisphere into any data distribution. We interpret the data points as electrical charges on the $z=0$ hyperplane in a space augmented with an additional dimension $z$, generating a high-dimensional electric field (the gradient of the solution to Poisson equation). We prove that if these charges flow upward along electric field lines, their initial distribution in the $z=0$ plane transforms into a distribution on the hemisphere of radius $r$ that becomes uniform in the $r \to\infty$ limit. To learn the bijective transformation, we estimate the normalized field in the augmented space. For sampling, we devise a backward ODE that is anchored by the physically meaningful additional dimension: the samples hit the unaugmented data manifold when the $z$ reaches zero. Experimentally, PFGM achieves current state-of-the-art performance among the normalizing flow models on CIFAR-10, with an Inception score of $9.68$ and a FID score of $2.35$. It also performs on par with the state-of-the-art SDE approaches while offering $10\times $ to $20 \times$ acceleration on image generation tasks. Additionally, PFGM appears more tolerant of estimation errors on a weaker network architecture and robust to the step size in the Euler method. The code is available at https://github.com/Newbeeer/poisson_flow .
We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for $N$ dimensional data by embedding paths in $N{+}D$ dimensional space while still controlling the progression with a simple scalar norm of the $D$ additional variables. The new models reduce to PFGM when $D{=}1$ and to diffusion models when $D{\to}\infty$. The flexibility of choosing $D$ allows us to trade off robustness against rigidity as increasing $D$ results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of $D$, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models ($D{\to} \infty$) to any finite $D$ values. Our experiments show that models with finite $D$ can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ $64{\times}64$ datasets, with FID scores of $1.91/2.43$ when $D{=}2048/128$. In class-conditional setting, $D{=}2048$ yields current state-of-the-art FID of $1.74$ on CIFAR-10. In addition, we demonstrate that models with smaller $D$ exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp
Generative processes that involve solving differential equations, such as diffusion models, frequently necessitate balancing speed and quality. ODE-based samplers are fast but plateau in performance while SDE-based samplers deliver higher sample quality at the cost of increased sampling time. We attribute this difference to sampling errors: ODE-samplers involve smaller discretization errors while stochasticity in SDE contracts accumulated errors. Based on these findings, we propose a novel sampling algorithm called Restart in order to better balance discretization errors and contraction. The sampling method alternates between adding substantial noise in additional forward steps and strictly following a backward ODE. Empirically, Restart sampler surpasses previous SDE and ODE samplers in both speed and accuracy. Restart not only outperforms the previous best SDE results, but also accelerates the sampling speed by 10-fold / 2-fold on CIFAR-10 / ImageNet $64 \times 64$. In addition, it attains significantly better sample quality than ODE samplers within comparable sampling times. Moreover, Restart better balances text-image alignment/visual quality versus diversity than previous samplers in the large-scale text-to-image Stable Diffusion model pre-trained on LAION $512 \times 512$. Code is available at https://github.com/Newbeeer/diffusion_restart_sampling
Mohamed Amine Ketata, Cedrik Laue, Ruslan Mammadov et al. · mit
Understanding how proteins structurally interact is crucial to modern biology, with applications in drug discovery and protein design. Recent machine learning methods have formulated protein-small molecule docking as a generative problem with significant performance boosts over both traditional and deep learning baselines. In this work, we propose a similar approach for rigid protein-protein docking: DiffDock-PP is a diffusion generative model that learns to translate and rotate unbound protein structures into their bound conformations. We achieve state-of-the-art performance on DIPS with a median C-RMSD of 4.85, outperforming all considered baselines. Additionally, DiffDock-PP is faster than all search-based methods and generates reliable confidence estimates for its predictions. Our code is publicly available at $\texttt{https://github.com/ketatam/DiffDock-PP}$
Bowen Jing, Hannes Stärk, Tommi Jaakkola et al. · mit
Molecular dynamics (MD) is a powerful technique for studying microscopic phenomena, but its computational cost has driven significant interest in the development of deep learning-based surrogate models. We introduce generative modeling of molecular trajectories as a paradigm for learning flexible multi-task surrogate models of MD from data. By conditioning on appropriately chosen frames of the trajectory, we show such generative models can be adapted to diverse tasks such as forward simulation, transition path sampling, and trajectory upsampling. By alternatively conditioning on part of the molecular system and inpainting the rest, we also demonstrate the first steps towards dynamics-conditioned molecular design. We validate the full set of these capabilities on tetrapeptide simulations and show that our model can produce reasonable ensembles of protein monomers. Altogether, our work illustrates how generative modeling can unlock value from MD data towards diverse downstream tasks that are not straightforward to address with existing methods or even MD itself. Code is available at https://github.com/bjing2016/mdgen.
Diffusion models generate samples by reversing a fixed forward diffusion process. Despite already providing impressive empirical results, these diffusion models algorithms can be further improved by reducing the variance of the training targets in their denoising score-matching objective. We argue that the source of such variance lies in the handling of intermediate noise-variance scales, where multiple modes in the data affect the direction of reverse paths. We propose to remedy the problem by incorporating a reference batch which we use to calculate weighted conditional scores as more stable training targets. We show that the procedure indeed helps in the challenging intermediate regime by reducing (the trace of) the covariance of training targets. The new stable targets can be seen as trading bias for reduced variance, where the bias vanishes with increasing reference batch size. Empirically, we show that the new objective improves the image quality, stability, and training speed of various popular diffusion models across datasets with both general ODE and SDE solvers. When used in combination with EDM, our method yields a current SOTA FID of 1.90 with 35 network evaluations on the unconditional CIFAR-10 generation task. The code is available at https://github.com/Newbeeer/stf
Guanhua Zhang, Jiabao Ji, Yang Zhang et al. · ibm-research
Image inpainting refers to the task of generating a complete, natural image based on a partially revealed reference image. Recently, many research interests have been focused on addressing this problem using fixed diffusion models. These approaches typically directly replace the revealed region of the intermediate or final generated images with that of the reference image or its variants. However, since the unrevealed regions are not directly modified to match the context, it results in incoherence between revealed and unrevealed regions. To address the incoherence problem, a small number of methods introduce a rigorous Bayesian framework, but they tend to introduce mismatches between the generated and the reference images due to the approximation errors in computing the posterior distributions. In this paper, we propose COPAINT, which can coherently inpaint the whole image without introducing mismatches. COPAINT also uses the Bayesian framework to jointly modify both revealed and unrevealed regions, but approximates the posterior distribution in a way that allows the errors to gradually drop to zero throughout the denoising steps, thus strongly penalizing any mismatches with the reference image. Our experiments verify that COPAINT can outperform the existing diffusion-based methods under both objective and subjective metrics. The codes are available at https://github.com/UCSB-NLP-Chang/CoPaint/.
Gabriele Corso, Hannes Stärk, Bowen Jing et al. · mit
Predicting the binding structure of a small molecule ligand to a protein -- a task known as molecular docking -- is critical to drug design. Recent deep learning methods that treat docking as a regression problem have decreased runtime compared to traditional search-based methods but have yet to offer substantial improvements in accuracy. We instead frame molecular docking as a generative modeling problem and develop DiffDock, a diffusion generative model over the non-Euclidean manifold of ligand poses. To do so, we map this manifold to the product space of the degrees of freedom (translational, rotational, and torsional) involved in docking and develop an efficient diffusion process on this space. Empirically, DiffDock obtains a 38% top-1 success rate (RMSD<2A) on PDBBind, significantly outperforming the previous state-of-the-art of traditional docking (23%) and deep learning (20%) methods. Moreover, while previous methods are not able to dock on computationally folded structures (maximum accuracy 10.4%), DiffDock maintains significantly higher precision (21.7%). Finally, DiffDock has fast inference times and provides confidence estimates with high selective accuracy.
Recent improvements in conditional generative modeling have made it possible to generate high-quality images from language descriptions alone. We investigate whether these methods can directly address the problem of sequential decision-making. We view decision-making not through the lens of reinforcement learning (RL), but rather through conditional generative modeling. To our surprise, we find that our formulation leads to policies that can outperform existing offline RL approaches across standard benchmarks. By modeling a policy as a return-conditional diffusion model, we illustrate how we may circumvent the need for dynamic programming and subsequently eliminate many of the complexities that come with traditional offline RL. We further demonstrate the advantages of modeling policies as conditional diffusion models by considering two other conditioning variables: constraints and skills. Conditioning on a single constraint or skill during training leads to behaviors at test-time that can satisfy several constraints together or demonstrate a composition of skills. Our results illustrate that conditional generative modeling is a powerful tool for decision-making.
Molecular conformer generation is a fundamental task in computational chemistry. Several machine learning approaches have been developed, but none have outperformed state-of-the-art cheminformatics methods. We propose torsional diffusion, a novel diffusion framework that operates on the space of torsion angles via a diffusion process on the hypertorus and an extrinsic-to-intrinsic score model. On a standard benchmark of drug-like molecules, torsional diffusion generates superior conformer ensembles compared to machine learning and cheminformatics methods in terms of both RMSD and chemical properties, and is orders of magnitude faster than previous diffusion-based models. Moreover, our model provides exact likelihoods, which we employ to build the first generalizable Boltzmann generator. Code is available at https://github.com/gcorso/torsional-diffusion.
Xuan Zhang, Limei Wang, Jacob Helwig et al. · cambridge, mit
Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This work aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science.
Victor Quach, Adam Fisch, Tal Schuster et al. · berkeley, mit
We propose a novel approach to conformal prediction for generative language models (LMs). Standard conformal prediction produces prediction sets -- in place of single predictions -- that have rigorous, statistical performance guarantees. LM responses are typically sampled from the model's predicted distribution over the large, combinatorial output space of natural language. Translating this process to conformal prediction, we calibrate a stopping rule for sampling different outputs from the LM that get added to a growing set of candidates until we are confident that the output set is sufficient. Since some samples may be low-quality, we also simultaneously calibrate and apply a rejection rule for removing candidates from the output set to reduce noise. Similar to conformal prediction, we prove that the sampled set returned by our procedure contains at least one acceptable answer with high probability, while still being empirically precise (i.e., small) on average. Furthermore, within this set of candidate responses, we show that we can also accurately identify subsets of individual components -- such as phrases or sentences -- that are each independently correct (e.g., that are not "hallucinations"), again with statistical guarantees. We demonstrate the promise of our approach on multiple tasks in open-domain question answering, text summarization, and radiology report generation using different LM variants.
To make effective decisions in novel environments with long-horizon goals, it is crucial to engage in hierarchical reasoning across spatial and temporal scales. This entails planning abstract subgoal sequences, visually reasoning about the underlying plans, and executing actions in accordance with the devised plan through visual-motor control. We propose Compositional Foundation Models for Hierarchical Planning (HiP), a foundation model which leverages multiple expert foundation model trained on language, vision and action data individually jointly together to solve long-horizon tasks. We use a large language model to construct symbolic plans that are grounded in the environment through a large video diffusion model. Generated video plans are then grounded to visual-motor control, through an inverse dynamics model that infers actions from generated videos. To enable effective reasoning within this hierarchy, we enforce consistency between the models via iterative refinement. We illustrate the efficacy and adaptability of our approach in three different long-horizon table-top manipulation tasks.
Protein structure prediction has reached revolutionary levels of accuracy on single structures, yet distributional modeling paradigms are needed to capture the conformational ensembles and flexibility that underlie biological function. Towards this goal, we develop EigenFold, a diffusion generative modeling framework for sampling a distribution of structures from a given protein sequence. We define a diffusion process that models the structure as a system of harmonic oscillators and which naturally induces a cascading-resolution generative process along the eigenmodes of the system. On recent CAMEO targets, EigenFold achieves a median TMScore of 0.84, while providing a more comprehensive picture of model uncertainty via the ensemble of sampled structures relative to existing methods. We then assess EigenFold's ability to model and predict conformational heterogeneity for fold-switching proteins and ligand-induced conformational change. Code is available at https://github.com/bjing2016/EigenFold.
Gabriele Corso, Yilun Xu, Valentin de Bortoli et al. · mit
In light of the widespread success of generative models, a significant amount of research has gone into speeding up their sampling time. However, generative models are often sampled multiple times to obtain a diverse set incurring a cost that is orthogonal to sampling time. We tackle the question of how to improve diversity and sample efficiency by moving beyond the common assumption of independent samples. We propose particle guidance, an extension of diffusion-based generative sampling where a joint-particle time-evolving potential enforces diversity. We analyze theoretically the joint distribution that particle guidance generates, how to learn a potential that achieves optimal diversity, and the connections with methods in other disciplines. Empirically, we test the framework both in the setting of conditional image generation, where we are able to increase diversity without affecting quality, and molecular conformer generation, where we reduce the state-of-the-art median error by 13% on average.
Jason Yim, Brian L. Trippe, Valentin De Bortoli et al. · oxford
The design of novel protein structures remains a challenge in protein engineering for applications across biomedicine and chemistry. In this line of work, a diffusion model over rigid bodies in 3D (referred to as frames) has shown success in generating novel, functional protein backbones that have not been observed in nature. However, there exists no principled methodological framework for diffusion on SE(3), the space of orientation preserving rigid motions in R3, that operates on frames and confers the group invariance. We address these shortcomings by developing theoretical foundations of SE(3) invariant diffusion models on multiple frames followed by a novel framework, FrameDiff, for learning the SE(3) equivariant score over multiple frames. We apply FrameDiff on monomer backbone generation and find it can generate designable monomers up to 500 amino acids without relying on a pretrained protein structure prediction network that has been integral to previous methods. We find our samples are capable of generalizing beyond any known protein structure.
Hannes Stärk, Bowen Jing, Regina Barzilay et al. · mit
A significant amount of protein function requires binding small molecules, including enzymatic catalysis. As such, designing binding pockets for small molecules has several impactful applications ranging from drug synthesis to energy storage. Towards this goal, we first develop HarmonicFlow, an improved generative process over 3D protein-ligand binding structures based on our self-conditioned flow matching objective. FlowSite extends this flow model to jointly generate a protein pocket's discrete residue types and the molecule's binding 3D structure. We show that HarmonicFlow improves upon state-of-the-art generative processes for docking in simplicity, generality, and average sample quality in pocket-level docking. Enabled by this structure modeling, FlowSite designs binding sites substantially better than baseline approaches.
This paper investigates Who's Harry Potter (WHP), a pioneering yet insufficiently understood method for LLM unlearning. We explore it in two steps. First, we introduce a new task of LLM targeted unlearning, where given an unlearning target (e.g., a person) and some unlearning documents, we aim to unlearn only the information about the target, rather than everything in the unlearning documents. We further argue that a successful unlearning should satisfy criteria such as not outputting gibberish, not fabricating facts about the unlearning target, and not releasing factual information under jailbreak attacks. Second, we construct a causal intervention framework for targeted unlearning, where the knowledge of the unlearning target is modeled as a confounder between LLM input and output, and the unlearning process as a deconfounding process. This framework justifies and extends WHP, deriving a simple unlearning algorithm that includes WHP as a special case. Experiments on existing and new datasets show that our approach, without explicitly optimizing for the aforementioned criteria, achieves competitive performance in all of them. Our code is available at https://github.com/UCSB-NLP-Chang/causal_unlearn.git.
Andrew Kirjner, Jason Yim, Raman Samusevich et al.
The ability to engineer novel proteins with higher fitness for a desired property would be revolutionary for biotechnology and medicine. Modeling the combinatorially large space of sequences is infeasible; prior methods often constrain optimization to a small mutational radius, but this drastically limits the design space. Instead of heuristics, we propose smoothing the fitness landscape to facilitate protein optimization. First, we formulate protein fitness as a graph signal then use Tikunov regularization to smooth the fitness landscape. We find optimizing in this smoothed landscape leads to improved performance across multiple methods in the GFP and AAV benchmarks. Second, we achieve state-of-the-art results utilizing discrete energy-based models and MCMC in the smoothed landscape. Our method, called Gibbs sampling with Graph-based Smoothing (GGS), demonstrates a unique ability to achieve 2.5 fold fitness improvement (with in-silico evaluation) over its training set. GGS demonstrates potential to optimize proteins in the limited data regime. Code: https://github.com/kirjner/GGS
Since diffusion models (DM) and the more recent Poisson flow generative models (PFGM) are inspired by physical processes, it is reasonable to ask: Can physical processes offer additional new generative models? We show that the answer is yes. We introduce a general family, Generative Models from Physical Processes (GenPhys), where we translate partial differential equations (PDEs) describing physical processes to generative models. We show that generative models can be constructed from s-generative PDEs (s for smooth). GenPhys subsume the two existing generative models (DM and PFGM) and even give rise to new families of generative models, e.g., "Yukawa Generative Models" inspired from weak interactions. On the other hand, some physical processes by default do not belong to the GenPhys family, e.g., the wave equation and the Schrödinger equation, but could be made into the GenPhys family with some modifications. Our goal with GenPhys is to explore and expand the design space of generative models.
Yilun Xu, Gabriele Corso, Tommi Jaakkola et al. · mit
Diffusion models (DMs) have revolutionized generative learning. They utilize a diffusion process to encode data into a simple Gaussian distribution. However, encoding a complex, potentially multimodal data distribution into a single continuous Gaussian distribution arguably represents an unnecessarily challenging learning problem. We propose Discrete-Continuous Latent Variable Diffusion Models (DisCo-Diff) to simplify this task by introducing complementary discrete latent variables. We augment DMs with learnable discrete latents, inferred with an encoder, and train DM and encoder end-to-end. DisCo-Diff does not rely on pre-trained networks, making the framework universally applicable. The discrete latents significantly simplify learning the DM's complex noise-to-data mapping by reducing the curvature of the DM's generative ODE. An additional autoregressive transformer models the distribution of the discrete latents, a simple step because DisCo-Diff requires only few discrete variables with small codebooks. We validate DisCo-Diff on toy data, several image synthesis tasks as well as molecular docking, and find that introducing discrete latents consistently improves model performance. For example, DisCo-Diff achieves state-of-the-art FID scores on class-conditioned ImageNet-64/128 datasets with ODE sampler.
Xiang Fu, Tian Xie, Andrew S. Rosen et al. · princeton
Metal-organic frameworks (MOFs) are of immense interest in applications such as gas storage and carbon capture due to their exceptional porosity and tunable chemistry. Their modular nature has enabled the use of template-based methods to generate hypothetical MOFs by combining molecular building blocks in accordance with known network topologies. However, the ability of these methods to identify top-performing MOFs is often hindered by the limited diversity of the resulting chemical space. In this work, we propose MOFDiff: a coarse-grained (CG) diffusion model that generates CG MOF structures through a denoising diffusion process over the coordinates and identities of the building blocks. The all-atom MOF structure is then determined through a novel assembly algorithm. Equivariant graph neural networks are used for the diffusion model to respect the permutational and roto-translational symmetries. We comprehensively evaluate our model's capability to generate valid and novel MOF structures and its effectiveness in designing outstanding MOF materials for carbon capture applications with molecular simulations.
Construction of a scaffold structure that supports a desired motif, conferring protein function, shows promise for the design of vaccines and enzymes. But a general solution to this motif-scaffolding problem remains open. Current machine-learning techniques for scaffold design are either limited to unrealistically small scaffolds (up to length 20) or struggle to produce multiple diverse scaffolds. We propose to learn a distribution over diverse and longer protein backbone structures via an E(3)-equivariant graph neural network. We develop SMCDiff to efficiently sample scaffolds from this distribution conditioned on a given motif; our algorithm is the first to theoretically guarantee conditional samples from a diffusion model in the large-compute limit. We evaluate our designed backbones by how well they align with AlphaFold2-predicted structures. We show that our method can (1) sample scaffolds up to 80 residues and (2) achieve structurally diverse scaffolds for a fixed motif.
Existing LLM-based automatic test generation methods mainly produce input and expected output pairs to categorize the intended behavior of correct programs. Although straightforward, these methods have limited diversity in generated tests and cannot provide enough debugging information. We propose HarnessLLM, a two-stage training pipeline that enables LLMs to write harness code for testing. Particularly, LLMs generate code that synthesizes inputs and validates the observed outputs, allowing complex test cases and flexible output validation such as invariant checking. To achieve this, we train LLMs with SFT followed by RLVR with a customized reward design. Experiments show that HarnessLLM outperforms input-output-based testing in bug finding and testing strategy diversity. HarnessLLM further benefits the code generation performance through test-time scaling with our generated test cases as inference-phase validation. Our code is available at https://github.com/UCSB-NLP-Chang/HarnessLLM.git.
Homa Esfahanizadeh, Adam Yala, Rafael G. L. D'Oliveira et al. · berkeley, mit
Allowing organizations to share their data for training of machine learning (ML) models without unintended information leakage is an open problem in practice. A promising technique for this still-open problem is to train models on the encoded data. Our approach, called Privately Encoded Open Datasets with Public Labels (PEOPL), uses a certain class of randomly constructed transforms to encode sensitive data. Organizations publish their randomly encoded data and associated raw labels for ML training, where training is done without knowledge of the encoding realization. We investigate several important aspects of this problem: We introduce information-theoretic scores for privacy and utility, which quantify the average performance of an unfaithful user (e.g., adversary) and a faithful user (e.g., model developer) that have access to the published encoded data. We then theoretically characterize primitives in building families of encoding schemes that motivate the use of random deep neural networks. Empirically, we compare the performance of our randomized encoding scheme and a linear scheme to a suite of computational attacks, and we also show that our scheme achieves competitive prediction accuracy to raw-sample baselines. Moreover, we demonstrate that multiple institutions, using independent random encoders, can collaborate to train improved ML models.
Selective classification allows models to abstain from making predictions (e.g., say "I don't know") when in doubt in order to obtain better effective accuracy. While typical selective models can be effective at producing more accurate predictions on average, they may still allow for wrong predictions that have high confidence, or skip correct predictions that have low confidence. Providing calibrated uncertainty estimates alongside predictions -- probabilities that correspond to true frequencies -- can be as important as having predictions that are simply accurate on average. However, uncertainty estimates can be unreliable for certain inputs. In this paper, we develop a new approach to selective classification in which we propose a method for rejecting examples with "uncertain" uncertainties. By doing so, we aim to make predictions with {well-calibrated} uncertainty estimates over the distribution of accepted examples, a property we call selective calibration. We present a framework for learning selectively calibrated models, where a separate selector network is trained to improve the selective calibration error of a given base model. In particular, our work focuses on achieving robust calibration, where the model is intentionally designed to be tested on out-of-domain data. We achieve this through a training strategy inspired by distributionally robust optimization, in which we apply simulated input perturbations to the known, in-domain training data. We demonstrate the empirical effectiveness of our approach on multiple image classification and lung cancer risk assessment tasks.
Computational antibody design seeks to automatically create an antibody that binds to an antigen. The binding affinity is governed by the 3D binding interface where antibody residues (paratope) closely interact with antigen residues (epitope). Thus, predicting 3D paratope-epitope complex (docking) is the key to finding the best paratope. In this paper, we propose a new model called Hierarchical Equivariant Refinement Network (HERN) for paratope docking and design. During docking, HERN employs a hierarchical message passing network to predict atomic forces and use them to refine a binding complex in an iterative, equivariant manner. During generation, its autoregressive decoder progressively docks generated paratopes and builds a geometric representation of the binding interface to guide the next residue choice. Our results show that HERN significantly outperforms prior state-of-the-art on paratope docking and design benchmarks.
Molecular dynamics (MD) simulation is essential for various scientific domains but computationally expensive. Learning-based force fields have made significant progress in accelerating ab-initio MD simulation but are not fast enough for many real-world applications due to slow inference for large systems and small time steps (femtosecond-level). We aim to address these challenges by learning a multi-scale graph neural network that directly simulates coarse-grained MD with a very large time step (nanosecond-level) and a novel refinement module based on diffusion models to mitigate simulation instability. The effectiveness of our method is demonstrated in two complex systems: single-chain coarse-grained polymers and multi-component Li-ion polymer electrolytes. For evaluation, we simulate trajectories much longer than the training trajectories for systems with different chemical compositions that the model is not trained on. Structural and dynamical properties can be accurately recovered at several orders of magnitude higher speed than classical force fields by getting out of the femtosecond regime.
Timur Garipov, Sebastiaan De Peuter, Ge Yang et al.
High training costs of generative models and the need to fine-tune them for specific tasks have created a strong interest in model reuse and composition. A key challenge in composing iterative generative processes, such as GFlowNets and diffusion models, is that to realize the desired target distribution, all steps of the generative process need to be coordinated, and satisfy delicate balance conditions. In this work, we propose Compositional Sculpting: a general approach for defining compositions of iterative generative processes. We then introduce a method for sampling from these compositions built on classifier guidance. We showcase ways to accomplish compositional sculpting in both GFlowNets and diffusion models. We highlight two binary operations $\unicode{x2014}$ the harmonic mean ($p_1 \otimes p_2$) and the contrast ($p_1 \unicode{x25D1}\,p_2$) between pairs, and the generalization of these operations to multiple component distributions. We offer empirical results on image and molecular generation tasks.
Bracha Laufer-Goldshtein, Adam Fisch, Regina Barzilay et al.
Machine learning applications frequently come with multiple diverse objectives and constraints that can change over time. Accordingly, trained models can be tuned with sets of hyper-parameters that affect their predictive behavior (e.g., their run-time efficiency versus error rate). As the number of constraints and hyper-parameter dimensions grow, naively selected settings may lead to sub-optimal and/or unreliable results. We develop an efficient method for calibrating models such that their predictions provably satisfy multiple explicit and simultaneous statistical guarantees (e.g., upper-bounded error rates), while also optimizing any number of additional, unconstrained objectives (e.g., total run-time cost). Building on recent results in distribution-free, finite-sample risk control for general losses, we propose Pareto Testing: a two-stage process which combines multi-objective optimization with multiple hypothesis testing. The optimization stage constructs a set of promising combinations on the Pareto frontier. We then apply statistical testing to this frontier only to identify configurations that have (i) high utility with respect to our objectives, and (ii) guaranteed risk levels with respect to our constraints, with specifiable high probability. We demonstrate the effectiveness of our approach to reliably accelerate the execution of large-scale Transformer models in natural language processing (NLP) applications. In particular, we show how Pareto Testing can be used to dynamically configure multiple inter-dependent model attributes -- including the number of layers computed before exiting, number of attention heads pruned, or number of text tokens considered -- to simultaneously control and optimize various accuracy and cost metrics.
We study the problem of aligning the supports of distributions. Compared to the existing work on distribution alignment, support alignment does not require the densities to be matched. We propose symmetric support difference as a divergence measure to quantify the mismatch between supports. We show that select discriminators (e.g. discriminator trained for Jensen-Shannon divergence) are able to map support differences as support differences in their one-dimensional output space. Following this result, our method aligns supports by minimizing a symmetrized relaxed optimal transport cost in the discriminator 1D space via an adversarial process. Furthermore, we show that our approach can be viewed as a limit of existing notions of alignment by increasing transportation assignment tolerance. We quantitatively evaluate the method across domain adaptation tasks with shifts in label distributions. Our experiments show that the proposed method is more robust against these shifts than other alignment-based baselines.
Ryotaro Okabe, Mouyang Cheng, Abhijatmedhi Chotrattanapituk et al.
Billions of organic molecules are known, but only a tiny fraction of the functional inorganic materials have been discovered, a particularly relevant problem to the community searching for new quantum materials. Recent advancements in machine-learning-based generative models, particularly diffusion models, show great promise for generating new, stable materials. However, integrating geometric patterns into materials generation remains a challenge. Here, we introduce Structural Constraint Integration in the GENerative model (SCIGEN). Our approach can modify any trained generative diffusion model by strategic masking of the denoised structure with a diffused constrained structure prior to each diffusion step to steer the generation toward constrained outputs. Furthermore, we mathematically prove that SCIGEN effectively performs conditional sampling from the original distribution, which is crucial for generating stable constrained materials. We generate eight million compounds using Archimedean lattices as prototype constraints, with over 10% surviving a multi-staged stability pre-screening. High-throughput density functional theory (DFT) on 26,000 survived compounds shows that over 50% passed structural optimization at the DFT level. Since the properties of quantum materials are closely related to geometric patterns, our results indicate that SCIGEN provides a general framework for generating quantum materials candidates.
Xiang Fu, Albert Musaelian, Anders Johansson et al.
The need to use a short time step is a key limit on the speed of molecular dynamics (MD) simulations. Simulations governed by classical potentials are often accelerated by using a multiple-time-step (MTS) integrator that evaluates certain potential energy terms that vary more slowly than others less frequently. This approach is enabled by the simple but limiting analytic forms of classical potentials. Machine learning interatomic potentials (MLIPs), in particular recent equivariant neural networks, are much more broadly applicable than classical potentials and can faithfully reproduce the expensive but accurate reference electronic structure calculations used to train them. They still, however, require the use of a single short time step, as they lack the inherent term-by-term scale separation of classical potentials. This work introduces a method to learn a scale separation in complex interatomic interactions by co-training two MLIPs. Initially, a small and efficient model is trained to reproduce short-time-scale interactions. Subsequently, a large and expressive model is trained jointly to capture the remaining interactions not captured by the small model. When running MD, the MTS integrator then evaluates the smaller model for every time step and the larger model less frequently, accelerating simulation. Compared to a conventionally trained MLIP, our approach can achieve a significant speedup (~3x in our experiments) without a loss of accuracy on the potential energy or simulation-derived quantities.
Many generative tasks in chemistry and science involve distributions invariant to group symmetries (e.g., permutation and rotation). A common strategy enforces invariance and equivariance through architectural constraints such as equivariant denoisers and invariant priors. In this paper, we challenge this tradition through the alternative canonicalization perspective: first map each sample to an orbit representative with a canonical pose or order, train an unconstrained (non-equivariant) diffusion or flow model on the canonical slice, and finally recover the invariant distribution by sampling a random symmetry transform at generation time. Building on a formal quotient-space perspective, our work provides a comprehensive theory of canonical diffusion by proving: (i) the correctness, universality and superior expressivity of canonical generative models over invariant targets; (ii) canonicalization accelerates training by removing diffusion score complexity induced by group mixtures and reducing conditional variance in flow matching. We then show that aligned priors and optimal transport act complementarily with canonicalization and further improves training efficiency. We instantiate the framework for molecular graph generation under $S_n \times SE(3)$ symmetries. By leveraging geometric spectra-based canonicalization and mild positional encodings, canonical diffusion significantly outperforms equivariant baselines in 3D molecule generation tasks, with similar or even less computation. Moreover, with a novel architecture Canon, CanonFlow achieves state-of-the-art performance on the challenging GEOM-DRUG dataset, and the advantage remains large in few-step generation.
Peter Holderrieth, Douglas Chen, Luca Eyring et al.
Flow and diffusion models produce high-quality samples, but adapting them to user preferences or constraints post-training remains costly and brittle, a challenge commonly called reward alignment. We argue that efficient reward alignment should be a property of the generative model itself, not an afterthought, and redesign the model for adaptability. We propose "Diamond Maps", stochastic flow map models that enable efficient and accurate alignment to arbitrary rewards at inference time. Diamond Maps amortize many simulation steps into a single-step sampler, like flow maps, while preserving the stochasticity required for optimal reward alignment. This design makes search, sequential Monte Carlo, and guidance scalable by enabling efficient and consistent estimation of the value function. Our experiments show that Diamond Maps can be learned efficiently via distillation from GLASS Flows, achieve stronger reward alignment performance, and scale better than existing methods. Our results point toward a practical route to generative models that can be rapidly adapted to arbitrary preferences and constraints at inference time.
Transition states (TSs) are central to understanding and quantitatively predicting chemical reactivity and reaction mechanisms. Although traditional TS generation methods are computationally expensive, recent generative modeling approaches have enabled chemically meaningful TS prediction for relatively small molecules. However, these methods fail to generalize to practically relevant reaction substrates because of distribution shifts induced by increasing molecular sizes. Furthermore, TS geometries for larger molecules are not available at scale, making it infeasible to train generative models from scratch on such molecules. To address these challenges, we introduce FragmentFlow: a divide-and-conquer approach that trains a generative model to predict TS geometries for the reactive core atoms, which define the reaction mechanism. The full TS structure is then reconstructed by re-attaching substituent fragments to the predicted core. By operating on reactive cores, whose size and composition remain relatively invariant across molecular contexts, FragmentFlow mitigates distribution shifts in generative modeling. Evaluated on a new curated dataset of reactions involving reactants with up to 33 heavy atoms, FragmentFlow correctly identifies 90% of TSs while requiring 30% fewer saddle-point optimization steps than classical initialization schemes. These results point toward scalable TS generation for high-throughput reactivity studies.
Bowen Jing, Gabriele Corso, Renato Berlinghieri et al.
Score-based models generate samples by mapping noise to data (and vice versa) via a high-dimensional diffusion process. We question whether it is necessary to run this entire process at high dimensionality and incur all the inconveniences thereof. Instead, we restrict the diffusion via projections onto subspaces as the data distribution evolves toward noise. When applied to state-of-the-art models, our framework simultaneously improves sample quality -- reaching an FID of 2.17 on unconditional CIFAR-10 -- and reduces the computational cost of inference for the same number of denoising steps. Our framework is fully compatible with continuous-time diffusion and retains its flexible capabilities, including exact log-likelihoods and controllable generation. Code is available at https://github.com/bjing2016/subspace-diffusion.
The biological functions of proteins often depend on dynamic structural ensembles. In this work, we develop a flow-based generative modeling approach for learning and sampling the conformational landscapes of proteins. We repurpose highly accurate single-state predictors such as AlphaFold and ESMFold and fine-tune them under a custom flow matching framework to obtain sequence-conditoned generative models of protein structure called AlphaFlow and ESMFlow. When trained and evaluated on the PDB, our method provides a superior combination of precision and diversity compared to AlphaFold with MSA subsampling. When further trained on ensembles from all-atom MD, our method accurately captures conformational flexibility, positional distributions, and higher-order ensemble observables for unseen proteins. Moreover, our method can diversify a static PDB structure with faster wall-clock convergence to certain equilibrium properties than replicate MD trajectories, demonstrating its potential as a proxy for expensive physics-based simulations. Code is available at https://github.com/bjing2016/alphaflow.
Hannes Stark, Bowen Jing, Chenyu Wang et al. · mit
Discrete diffusion or flow models could enable faster and more controllable sequence generation than autoregressive models. We show that naïve linear flow matching on the simplex is insufficient toward this goal since it suffers from discontinuities in the training target and further pathologies. To overcome this, we develop Dirichlet flow matching on the simplex based on mixtures of Dirichlet distributions as probability paths. In this framework, we derive a connection between the mixtures' scores and the flow's vector field that allows for classifier and classifier-free guidance. Further, we provide distilled Dirichlet flow matching, which enables one-step sequence generation with minimal performance hits, resulting in $O(L)$ speedups compared to autoregressive models. On complex DNA sequence generation tasks, we demonstrate superior performance compared to all baselines in distributional metrics and in achieving desired design targets for generated sequences. Finally, we show that our classifier-free guidance approach improves unconditional generation and is effective for generating DNA that satisfies design targets. Code is available at https://github.com/HannesStark/dirichlet-flow-matching.
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
Multimodal representation learning seeks to relate and decompose information inherent in multiple modalities. By disentangling modality-specific information from information that is shared across modalities, we can improve interpretability and robustness and enable downstream tasks such as the generation of counterfactual outcomes. Separating the two types of information is challenging since they are often deeply entangled in many real-world applications. We propose Disentangled Self-Supervised Learning (DisentangledSSL), a novel self-supervised approach for learning disentangled representations. We present a comprehensive analysis of the optimality of each disentangled representation, particularly focusing on the scenario not covered in prior work where the so-called Minimum Necessary Information (MNI) point is not attainable. We demonstrate that DisentangledSSL successfully learns shared and modality-specific features on multiple synthetic and real-world datasets and consistently outperforms baselines on various downstream tasks, including prediction tasks for vision-language data, as well as molecule-phenotype retrieval tasks for biological data. The code is available at https://github.com/uhlerlab/DisentangledSSL.
Recent studies have identified one aggravating factor of LLM hallucinations as the knowledge inconsistency between pre-training and fine-tuning, where unfamiliar fine-tuning data mislead the LLM to fabricate plausible but wrong outputs. In this paper, we propose a novel fine-tuning strategy called Prereq-Tune to address this knowledge inconsistency and reduce hallucinations. Fundamentally, Prereq-Tune disentangles the learning of skills and knowledge, so the model learns only the task skills without being impacted by the knowledge inconsistency. To achieve this, Prereq-Tune introduces an additional prerequisite learning stage to learn the necessary knowledge for SFT, allowing subsequent SFT to focus only on task skills. Prereq-Tune can also be combined with fictitious synthetic data to enhance the grounding of LLM outputs to their internal knowledge. Experiments show that Prereq-Tune outperforms existing baselines in improving LLM's factuality across short QA and long-form generation tasks. It also opens new possibilities for knowledge-controlled generation in LLMs. Our code is available at https://github.com/UCSB-NLP-Chang/Prereq_tune.git.
Molecular docking is critical to structure-based virtual screening, yet the throughput of such workflows is limited by the expensive optimization of scoring functions involved in most docking algorithms. We explore how machine learning can accelerate this process by learning a scoring function with a functional form that allows for more rapid optimization. Specifically, we define the scoring function to be the cross-correlation of multi-channel ligand and protein scalar fields parameterized by equivariant graph neural networks, enabling rapid optimization over rigid-body degrees of freedom with fast Fourier transforms. The runtime of our approach can be amortized at several levels of abstraction, and is particularly favorable for virtual screening settings with a common binding pocket. We benchmark our scoring functions on two simplified docking-related tasks: decoy pose scoring and rigid conformer docking. Our method attains similar but faster performance on crystal structures compared to the widely-used Vina and Gnina scoring functions, and is more robust on computationally predicted structures. Code is available at https://github.com/bjing2016/scalar-fields.
Annealing-based neural samplers seek to amortize sampling from unnormalized distributions by training neural networks to transport a family of densities interpolating from source to target. A crucial design choice in the training phase of such samplers is the proposal distribution by which locations are generated at which to evaluate the loss. Previous work has obtained such a proposal distribution by combining a partially learned transport with annealed Langevin dynamics. However, isolated modes and other pathological properties of the annealing path imply that such proposals achieve insufficient exploration and thereby lower performance post training. To remedy this, we propose continuously tempered diffusion samplers, which leverage exploration techniques developed in the context of molecular dynamics to improve proposal distributions. Specifically, a family of distributions across different temperatures is introduced to lower energy barriers at higher temperatures and drive exploration at the lower temperature of interest. We empirically validate improved sampler performance driven by extended exploration. Code is available at https://github.com/eje24/ctds.
Generative models have made significant impacts across various domains, largely due to their ability to scale during training by increasing data, computational resources, and model size, a phenomenon characterized by the scaling laws. Recent research has begun to explore inference-time scaling behavior in Large Language Models (LLMs), revealing how performance can further improve with additional computation during inference. Unlike LLMs, diffusion models inherently possess the flexibility to adjust inference-time computation via the number of denoising steps, although the performance gains typically flatten after a few dozen. In this work, we explore the inference-time scaling behavior of diffusion models beyond increasing denoising steps and investigate how the generation performance can further improve with increased computation. Specifically, we consider a search problem aimed at identifying better noises for the diffusion sampling process. We structure the design space along two axes: the verifiers used to provide feedback, and the algorithms used to find better noise candidates. Through extensive experiments on class-conditioned and text-conditioned image generation benchmarks, our findings reveal that increasing inference-time compute leads to substantial improvements in the quality of samples generated by diffusion models, and with the complicated nature of images, combinations of the components in the framework can be specifically chosen to conform with different application scenario.
Despite diffusion models' superior capabilities in modeling complex distributions, there are still non-trivial distributional discrepancies between generated and ground-truth images, which has resulted in several notable problems in image generation, including missing object errors in text-to-image generation and low image quality. Existing methods that attempt to address these problems mostly do not tend to address the fundamental cause behind these problems, which is the distributional discrepancies, and hence achieve sub-optimal results. In this paper, we propose a particle filtering framework that can effectively address both problems by explicitly reducing the distributional discrepancies. Specifically, our method relies on a set of external guidance, including a small set of real images and a pre-trained object detector, to gauge the distribution gap, and then design the resampling weight accordingly to correct the gap. Experiments show that our methods can effectively correct missing object errors and improve image quality in various image generation tasks. Notably, our method outperforms the existing strongest baseline by 5% in object occurrence and 1.0 in FID on MS-COCO. Our code is publicly available at https://github.com/UCSB-NLP-Chang/diffusion_resampling.git.
We propose to identify directions invariant to a given classifier so that these directions can be controlled in tasks such as style transfer. While orthogonal decomposition is directly identifiable when the given classifier is linear, we formally define a notion of orthogonality in the non-linear case. We also provide a surprisingly simple method for constructing the orthogonal classifier (a classifier utilizing directions other than those of the given classifier). Empirically, we present three use cases where controlling orthogonal variation is important: style transfer, domain adaptation, and fairness. The orthogonal classifier enables desired style transfer when domains vary in multiple aspects, improves domain adaptation with label shifts and mitigates the unfairness as a predictor. The code is available at http://github.com/Newbeeer/orthogonal_classifier
Selective rationalization explains the prediction of complex neural networks by finding a small subset of the input that is sufficient to predict the neural model output. The selection mechanism is commonly integrated into the model itself by specifying a two-component cascaded system consisting of a rationale generator, which makes a binary selection of the input features (which is the rationale), and a predictor, which predicts the output based only on the selected features. The components are trained jointly to optimize prediction performance. In this paper, we reveal a major problem with such cooperative rationalization paradigm -- model interlocking. Interlocking arises when the predictor overfits to the features selected by the generator thus reinforcing the generator's selection even if the selected rationales are sub-optimal. The fundamental cause of the interlocking problem is that the rationalization objective to be minimized is concave with respect to the generator's selection policy. We propose a new rationalization framework, called A2R, which introduces a third component into the architecture, a predictor driven by soft attention as opposed to selection. The generator now realizes both soft and hard attention over the features and these are fed into the two different predictors. While the generator still seeks to support the original predictor performance, it also minimizes a gap between the two predictors. As we will show theoretically, since the attention-based predictor exhibits a better convexity property, A2R can overcome the concavity barrier. Our experiments on two synthetic benchmarks and two real datasets demonstrate that A2R can significantly alleviate the interlock problem and find explanations that better align with human judgments. We release our code at https://github.com/Gorov/Understanding_Interlocking.
Ensuring generalization to unseen environments remains a challenge. Domain shift can lead to substantially degraded performance unless shifts are well-exercised within the available training environments. We introduce a simple robust estimation criterion -- transfer risk -- that is specifically geared towards optimizing transfer to new environments. Effectively, the criterion amounts to finding a representation that minimizes the risk of applying any optimal predictor trained on one environment to another. The transfer risk essentially decomposes into two terms, a direct transfer term and a weighted gradient-matching term arising from the optimality of per-environment predictors. Although inspired by IRM, we show that transfer risk serves as a better out-of-distribution generalization criterion, both theoretically and empirically. We further demonstrate the impact of optimizing such transfer risk on two controlled settings, each representing a different pattern of environment shift, as well as on two real-world datasets. Experimentally, the approach outperforms baselines across various out-of-distribution generalization tasks. Code is available at \url{https://github.com/Newbeeer/TRM}.