We propose LEAPS, an algorithm to sample from discrete distributions known up to normalization by learning a rate matrix of a continuous-time Markov chain (CTMC). LEAPS can be seen as a continuous-time formulation of annealed importance sampling and sequential Monte Carlo methods, extended so that the variance of the importance weights is offset by the inclusion of the CTMC. To derive these importance weights, we introduce a set of Radon-Nikodym derivatives of CTMCs over their path measures. Because the computation of these weights is intractable with standard neural network parameterizations of rate matrices, we devise a new compact representation for rate matrices via what we call locally equivariant functions. To parameterize them, we introduce a family of locally equivariant multilayer perceptrons, attention layers, and convolutional networks, and provide an approach to make deep networks that preserve the local equivariance. This property allows us to propose a scalable training algorithm for the rate matrix such that the variance of the importance weights associated to the CTMC are minimal. We demonstrate the efficacy of LEAPS on problems in statistical physics.

We introduce generator matching, a modality-agnostic framework for generative modeling using arbitrary Markov processes. Generators characterize the infinitesimal evolution of a Markov process, which we leverage for generative modeling in a similar vein to flow matching: we construct conditional generators which generate single data points, then learn to approximate the marginal generator which generates the full data distribution. We show that generator matching unifies various generative modeling methods, including diffusion models, flow matching and discrete diffusion models. Furthermore, it provides the foundation to expand the design space to new and unexplored Markov processes such as jump processes. Finally, generator matching enables the construction of superpositions of Markov generative processes and enables the construction of multimodal models in a rigorous manner. We empirically validate our method on protein and image structure generation, showing that superposition with a jump process improves image generation.

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 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. SSL 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. Humans understand and interact with the world using multiple senses, each providing unique and complementary information essential for forming a comprehensive mental representation of the environment. Large multimodal representation learning models such as CLIP (Radford et al., 2021), trained through self-supervised learning, maximally capture the mutual information shared across multiple modalities, exploiting the assumption of multi-view redundancy (Tosh et al., 2021; Sridharan & Kakade, 2008). This property indicates that shared information between modalities is exactly what is relevant for downstream tasks. However, the modality gap, rooted in the inherent differences in representational nature and information content across modalities (Liang et al., 2022b; Ramasinghe et al., 2024; Huh et al., 2024), leads to the misalignment between modalities and restricts the application of these methods in many real-world multimodal scenarios.

Classical Hamiltonian mechanics has been widely used in machine learning in the form of Hamiltonian Monte Carlo for applications with predetermined force fields. In this work, we explore the potential of deliberately designing force fields for Hamiltonian ODEs, introducing Hamiltonian velocity predictors (HVPs) as a tool for score matching and generative models. We present two innovations constructed with HVPs: Hamiltonian Score Matching (HSM), which estimates score functions by augmenting data via Hamiltonian trajectories, and Hamiltonian Generative Flows (HGFs), a novel generative model that encompasses diffusion models and flow matching as HGFs with zero force fields. We showcase the extended design space of force fields by introducing Oscillation HGFs, a generative model inspired by harmonic oscillators. Our experiments validate our theoretical insights about HSM as a novel score matching metric and demonstrate that HGFs rival leading generative modeling techniques.

Efficiently processing structured point cloud data while preserving multiscale information is a key challenge across domains, from graphics to atomistic modeling. Using a curated dataset of simulated galaxy positions and properties, represented as point clouds, we benchmark the ability of graph neural networks to simultaneously capture local clustering environments and long-range correlations. Given the homogeneous and isotropic nature of the Universe, the data exhibits a high degree of symmetry. We therefore focus on evaluating the performance of Euclidean symmetry-preserving ($E(3)$-equivariant) graph neural networks, showing that they can outperform non-equivariant counterparts and domain-specific information extraction techniques in downstream performance as well as simulation-efficiency. However, we find that current architectures fail to capture information from long-range correlations as effectively as domain-specific baselines, motivating future work on architectures better suited for extracting long-range information.

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. It also opens new possibilities for knowledge-controlled generation in LLMs. Hallucination of large language models (LLMs) refers to the phenomenon where LLMs' outputs look plausible but diverge from real-world facts. It has become a major concern of LLMs, seriously undermining their reliability and trustworthiness (Huang et al., 2023; Ji et al., 2023). Recent research has unveiled one aggravating factor of LLM hallucination, which is the knowledge inconsistency between the pre-training and tuning (e.g., instruction-or fine-tuning) stages (Gekhman et al., 2024; Kang et al., 2024; Lin et al., 2024). More specifically, if the tuning stage involves training examples that require knowledge that an LLM has not seen during pre-training, then the LLM would be misled to fabricate plausible but wrong answers to unfamiliar questions (Schulman, 2023; Gao, 2021; Goldberg, 2023). For example, consider fine-tuning a model for a question answering (QA) task with the example'When was John Estes born?' and assume that the LLM has never learned about John Estes during pre-training. However, since the LLM is still trained to produce the correct answer, '1987', it is consequently encouraged to respond with a random legitimate year whenever it is asked about the birth year of any unknown person, thus giving rise to hallucination. These findings highlight an important but previously understudied consideration of LLM training, which is the disentanglement between knowledge and skill. Specifically, it is discovered that knowledge and skills are acquired at different stages of LLM training, the former at pre-training, and the latter at tuning (Zhou et al., 2023; Gudibande et al., 2024). However, although the focus in the tuning stage is to learn skills, not knowledge, the learning process is still interfered with by any inconsistency in the knowledge aspect, because the information on the two aspects is entangled.

Recent studies have demonstrated the strong empirical performance of diffusion models on discrete sequences (i.e., discrete diffusion models) across domains from natural language to biological sequence generation. For example, in the protein inverse folding task, where the goal is to generate a protein sequence from a given backbone structure, conditional diffusion models have achieved impressive results in generating natural-like sequences that fold back into the original structure. However, practical design tasks often require not only modeling a conditional distribution but also optimizing specific task objectives. For instance, in the inverse folding task, we may prefer protein sequences with high stability. To address this, we consider the scenario where we have pre-trained discrete diffusion models that can generate natural-like sequences, as well as reward models that map sequences to task objectives. We then formulate the reward maximization problem within discrete diffusion models, analogous to reinforcement learning (RL), while minimizing the KL divergence against pretrained diffusion models to preserve naturalness. To solve this RL problem, we propose a novel algorithm, DRAKES, that enables direct backpropagation of rewards through entire trajectories generated by diffusion models, by making the originally nondifferentiable trajectories differentiable using the Gumbel-Softmax trick. Our theoretical analysis indicates that our approach can generate sequences that are both natural-like (i.e., have a high probability under a pretrained model) and yield high rewards. While similar tasks have been recently explored in diffusion models for continuous domains, our work addresses unique algorithmic and theoretical challenges specific to discrete diffusion models, which arise from their foundation in continuous-time Markov chains rather than Brownian motion. Finally, we demonstrate the effectiveness of our algorithm in generating DNA and protein sequences that optimize enhancer activity and protein stability, respectively, important tasks for gene therapies and protein-based therapeutics. Diffusion models have gained widespread recognition as effective generative models in continuous spaces, such as image and video generation (Song et al., 2020; Ho et al., 2022). Inspired by seminal works (e.g., Austin et al. (2021); Campbell et al. (2022); Sun et al. (2022)), recent studies (Lou et al., 2023; Shi et al., 2024; Sahoo et al., 2024) have shown that diffusion models are also highly effective in discrete spaces, including natural language and biological sequence generation (DNA, RNA, proteins). Work mainly done during an internship at Genentech.

Discrete diffusion has achieved state-of-the-art performance, outperforming or approaching autoregressive models on standard benchmarks. In this work, we introduce Discrete Diffusion with Planned Denoising (DDPD), a novel framework that separates the generation process into two models: a planner and a denoiser. At inference time, the planner selects which positions to denoise next by identifying the most corrupted positions in need of denoising, including both initially corrupted and those requiring additional refinement. This plan-and-denoise approach enables more efficient reconstruction during generation by iteratively identifying and denoising corruptions in the optimal order. DDPD outperforms traditional denoiser-only mask diffusion methods, achieving superior results on language modeling benchmarks such as text8, OpenWebText, and token-based generation on ImageNet $256 \times 256$. Notably, in language modeling, DDPD significantly reduces the performance gap between diffusion-based and autoregressive methods in terms of generative perplexity. Code is available at https://github.com/liusulin/DDPD.

Rationally identifying variables responsible for changes to a biological system can enable myriad applications in disease understanding and cell engineering. From a causality perspective, we are given two datasets generated by the same causal model, one observational (control) and one interventional (perturbed). The goal is to isolate the subset of measured variables (e.g. genes) that were the targets of the intervention, i.e. those whose conditional independencies have changed. Knowing the causal graph would limit the search space, allowing us to efficiently pinpoint these variables. However, current algorithms that infer causal graphs in the presence of unknown intervention targets scale poorly to the hundreds or thousands of variables in biological data, as they must jointly search the combinatorial spaces of graphs and consistent intervention targets. In this work, we propose a causality-inspired approach for predicting perturbation targets that decouples the two search steps. First, we use an amortized causal discovery model to separately infer causal graphs from the observational and interventional datasets. Then, we learn to map these paired graphs to the sets of variables that were intervened upon, in a supervised learning framework. This approach consistently outperforms baselines for perturbation modeling on seven single-cell transcriptomics datasets, each with thousands of measured variables. We also demonstrate significant improvements over six causal discovery algorithms in predicting intervention targets across a variety of tractable, synthetic datasets.

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.