Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

Capturing the structural changes that molecules undergo during chemical reactions in real space and time is a long-standing dream and an essential prerequisite for understanding and ultimately controlling femtochemistry. A key approach to tackle this challenging task is Coulomb explosion imaging, which has benefited decisively from recently emerging high-repetition-rate X-ray free-electron laser sources. With this technique, information on the molecular structure is inferred from the momentum distributions of the ions produced by the rapid Coulomb explosion of molecules. Retrieving molecular structures from these distributions poses a highly nonlinear inverse problem that remains unsolved for molecules consisting of more than a few atoms. Here, we address this challenge using a diffusion-based Transformer neural network. We show that the network reconstructs unknown molecular geometries from ion-momentum distributions with a mean absolute error below one Bohr radius, which is half the length of a typical chemical bond.

Operational disaster response goes beyond damage assessment, requiring responders to integrate multi-sensor signals, reason over road networks, populations and key facilities, plan evacuations, and produce actionable reports. However, prior work largely isolates remote-sensing perception or evaluates generic tool use, leaving the end-to-end workflows of emergency operations underexplored. In this paper, we introduce Disaster Operational Response Agent benchmark (DORA), the first agentic benchmark for end-to-end disaster response: 515 expert-authored tasks across 45 real-world disaster events spanning 10 types, paired with expert-verified, replayable gold trajectories totaling 3,500 tool-call steps. Tasks span five dimensions that cover the operational disaster-response pipeline: disaster perception, spatial relational analysis, rescue and evacuation planning, temporal evolution reasoning, and multi-modal report synthesis. Agents compose calls from a 108-tool MCP library over heterogeneous geospatial data: optical, SAR, and multi-spectral imagery across single-, bi-, and multi-temporal sequences (0.015-10m GSD), complemented by elevation and social vector layers. We comprehensively evaluate 13 frontier LLMs on our benchmark, revealing three persistent challenges: 1) disaster-domain grounding exposes unique failure modes (damage-semantic grounding, sensor-modality mismatch, and disaster-pipeline composition); 2) agents are doubly bottlenecked by tool selection and argument grounding, where gold tool-order hints improve accuracy by only 1.08-4.40

MeanFlow (MF) is a diffusion-motivated generative model that enables efficient few-step generation by learning long jumps directly from noise to data. In practice, it is often used as a latent MF by leveraging the pre-trained Stable Diffusion variational autoencoder (SD-VAE) for high-dimensional data modeling. However, MF training remains computationally demanding and is often unstable. During inference, the SD-VAE decoder dominates the generation cost, and MF depends on complex guidance hyperparameters for class-conditional generation. In this work, we develop an efficient training and sampling scheme for MF in the latent space of a Representation Autoencoder (RAE), where a pre-trained vision encoder (e.g., DINO) provides semantically rich latents paired with a lightweight decoder. We observe that naive MF training in the RAE latent space suffers from severe gradient explosion. To stabilize and accelerate training, we adopt Consistency Mid-Training for trajectory-aware initialization and use a two-stage scheme: distillation from a pre-trained flow matching teacher to speed convergence and reduce variance, followed by an optional bootstrapping stage with a one-point velocity estimator to further reduce deviation from the oracle mean flow. This design removes the need for guidance, simplifies training configurations, and reduces computation in both training and sampling. Empirically, our method achieves a 1-step FID of 2.03, outperforming vanilla MF’s 3.43, while reducing sampling GFLOPS by 38% and total training cost by 83% on ImageNet 256. We further scale our approach to ImageNet 512, achieving a competitive one-step FID of 3.23 with the lowest GFLOPS among all baselines.Code and proofs are available in the supplementary material.

Diffusion models and flow-based methods have shown impressive generative capability, especially for images, but their sampling is expensive because it requires many iterative updates. We introduce W-Flow, a framework for training a generator that transforms samples from a simple reference distribution into samples from a target data distribution in a single step. This is achieved in two steps: we first define an evolution from the reference distribution to the target distribution through a Wasserstein gradient flow that minimizes an energy functional; second, we train a static neural generator to compress this evolution into one-step generation. We instantiate the energy functional with the Sinkhorn divergence, which yields an efficient optimal-transport-based update rule that captures global distributional discrepancy and improves coverage of the target distribution. We further prove that the finite-sample training dynamics converge to the continuous-time distributional dynamics under suitable assumptions. Empirically, W-Flow sets a new state of the art for one-step ImageNet 256×256 generation, achieving 1.29 FID, with improved mode coverage and domain transfer. Compared to multi-step diffusion models with similar FID scores, our method yields approximately 100× faster sampling. These results show that Wasserstein gradient flows provide a principled and effective foundation for fast and high-fidelity generative modeling.

This article provides an introduction to the mathematical foundations and algorithmic frameworks used to align large language models (LLMs) with human intentions, preferences, and values. We discuss standard alignment techniques, such as supervised fine-tuning (SFT), reinforcement learning with human feedback (RLHF), and direct preference optimization (DPO). We also explore the theoretical underpinnings of learning from human preferences, drawing connections to inverse reinforcement learning (IRL), and discrete choice models. We present state-of-the-art algorithms in a tutorial style, discuss their advantages and limitations, and offer insights into practical implementation. Our exposition is intended to serve as a comprehensive resource for researchers and practitioners, providing both a foundational understanding of alignment methodologies and a framework for developing more robust and scalable alignment techniques.

Discrete diffusion models have demonstrated great promise in modeling various sequence data, ranging from human language to biological sequences. Inspired by the success of RL in language models, there is growing interest in further improving the models by alignment with a certain reward. In this work, we propose an offline preference optimization method to approach trajectory alignment for discrete diffusion models. Instead of applying the reward on the final output and backpropagating the gradient to the entire denoising process, we decompose the problem into a set of stepwise alignment objectives by matching the per-step posterior. This framework enables efficient diffusion optimization, is compatible with arbitrary reward functions, and importantly, yields an equivalent optimal solution under additive factorization of the trajectory reward. Experiments across multiple domains including DNA sequence design, protein inverse folding, and language modeling consistently demonstrate the superiority of our approach. Notably, it achieves an up to 12\% improvement over the most competitive RL-based baseline in terms of predicted activity on DNA sequence design, and further improves the GSM8K score from 78.6 to 81.2 on LLaDA-8B-Instruct for language modeling.

Adversarial diffusion and diffusion-inversion methods have advanced unpaired image-to-image translation, but each faces key limitations. Adversarial approaches require target-domain adversarial loss during training, which can limit generalization to unseen data, while diffusion-inversion methods often produce low-fidelity translations due to imperfect inversion into noise-latent representations. In this work, we propose the Self-Supervised Semantic Bridge (SSB), a versatile framework that integrates external semantic priors into diffusion bridge models to enable spatially faithful translation without cross-domain supervision. Our key idea is to leverage self-supervised visual encoders to learn representations that are invariant to appearance changes but capture geometric structure, forming a shared latent space that conditions the diffusion bridges. Extensive experiments show that SSB outperforms strong prior methods for challenging medical image synthesis in both in-domain and out-of-domain settings, and extends easily to high-quality text-guided editing.

Generations from large language models often fail to conform to desired constraints such as JSON schema. Existing locally constrained decoding (LCD) approaches enforce constraints by myopically masking out next tokens, resulting in biased sampling and degradation in performance. Recent work uses sequential Monte Carlo (SMC) methods to mitigate such biases, but designing effective proposal distributions or potential functions remains a key challenge. In this work, we propose a generic approach to construct proposals and potentials for SMC sampling from p_lm( ·|constraint). First, we show that constraints specified as finite automata can be tensorized for efficient execution on GPUs, which we use to construct globally constrained decoding (GCD) proposals. In addition, leveraging the fact that tensorized finite automata share the same circuit structure as hidden Markov models, we circuit-multiply them to obtain the probabilistic GCD (P-GCD) proposals encoding both logical and probabilistic information about the target distributions. We evaluate (P-)GCD on the tasks of function calling, keyword-based generation, and SQL generation. Experiments show that under the same SMC sampling setup, compared to LCD proposals, (P-)GCD converges faster to the target distribution with significantly fewer particles.

Diffusion models have become the dominant tool for high-fidelity image and video generation, yet are critically bottlenecked by their inference speed due to the numerous iterative passes of Diffusion Transformers. To reduce the exhaustive compute, recent works resort to the feature caching and reusing scheme that skips network evaluations at selected diffusion steps by using cached features in previous steps. However, their preliminary design solely relies on local approximation, causing errors to grow rapidly with large skips and leading to degraded sample quality at high speedups. In this work, we propose spectral diffusion feature forecaster (Spectrum), a training-free approach that enables global, long-range feature reuse with tightly controlled error. In particular, we view the latent features of the denoiser as functions over time and approximate them with Chebyshev polynomials. Specifically, we fit the coefficient for each basis via ridge regression, which is then leveraged to forecast features at multiple future diffusion steps. We theoretically reveal that our approach admits more favorable long-horizon behavior and yields an error bound that does not compound with the step size. Extensive experiments on various state-of-the-art image and video diffusion models consistently verify the superiority of our approach. Notably, we achieve up to 4.79× speedup on FLUX.1 and 4.67× speedup on Wan2.1-14B, while maintaining much higher sample quality compared with the baselines.

Constrained decoding is essential for serving LLMs, ensuring that generated outputs follow specific structures such as JSON schema-formatted function calls. Existing systems are designed for autoregressive models and assume left-to-right generation, masking out invalid next tokens at each step. Diffusion language models, however, break this assumption: they sample multiple positions simultaneously from a fully-factorized mean-field distribution at each denoising step. In this paper, we present an exact and tractable algorithm for sampling from the constrained mean-field posterior under any constraint expressible as a finite automaton. Viewing finite automata as graphical models, we obtain tractable representations of the constrained distribution that enable efficient inference. The approach guarantees constraint satisfaction by construction, supports both greedy and sampling-based decoding, and is compatible with parallel and block-wise decoding under arbitrary remasking schedules. Applying depth-reduction techniques from arithmetic circuit theory, we further reduce sampling depth from linear to logarithmic in the sequence length. Empirical evaluations on Dream-7B and LLaDA-8B show substantial accuracy gains across various tasks including function calling (xLAM, BFCL), planning (Sudoku, Countdown), text-to-SQL (Spider), and math reasoning (GSM-Symbolic), with little inference overhead relative to unconstrained decoding. For example, on BFCL-Live, our approach improves Dream-7B's greedy decoding accuracy from 63.9

Online reinforcement learning (RL) has been central to post-training language models, but its extension to diffusion models remains challenging due to intractable likelihoods. Recent works discretize the reverse sampling process to enable GRPO-style training, yet they inherit fundamental drawbacks. These include solver restrictions, forward–reverse inconsistency, and complicated integration with classifier-free guidance (CFG). We introduce Diffusion Negative-aware FineTuning (DiffusionNFT), a new online RL paradigm that optimizes diffusion models directly on the forward process via flow matching. DiffusionNFT contrasts positive and negative generations to define an implicit policy improvement direction, naturally incorporating reinforcement signals into the supervised learning objective. This formulation enables training with arbitrary black-box solvers, eliminates the need for likelihood estimation, and requires only clean images rather than sampling trajectories for policy optimization. DiffusionNFT is up to $25\times$ more efficient than FlowGRPO in head-to-head comparisons, while being CFG-free. For instance, DiffusionNFT improves the GenEval score from 0.24 to 0.98 within 1k steps, while FlowGRPO achieves 0.95 with over 5k steps and additional CFG employment. By leveraging multiple reward models, DiffusionNFT significantly boosts the performance of SD3.5-Medium in every benchmark tested.

Diffusion models can feel like a jungle of acronyms, but the core idea is simple: start from noise and gradually move a cloud of samples until it looks like real data. This post gives an intuition-first tour showing that DDPMs, score-based models, and flow matching are the same recipe with different prediction targets, all rooted in the change-of-variable rule from calculus and powered by one shared “conditional trick” that turns learning into supervised regression. Finally, we zoom out to the speed problem and show how flow map models aim to replace many tiny denoising steps with a few big, accurate jumps toward real-time generation.

Diffusion Language Models (DLMs) offer order-agnostic generation that can explore many possible decoding trajectories. However, current decoding methods commit to a single trajectory, limiting exploration in trajectory space. We introduce Order-Token Search to explore this space through jointly searching over generation order and token values. Its core is a likelihood estimator that scores denoising actions, enabling stable pruning and efficient exploration of diverse trajectories. Across mathematical reasoning and coding benchmarks, Order-Token Search consistently outperforms baselines on GSM8K, MATH500, Countdown, and HumanEval (3.1

Bayesian optimization (BO) is a common framework for optimizing black-box functions, yet most existing methods assume static query costs and rely on myopic acquisition strategies. We introduce LookaHES, a nonmyopic BO framework designed for dynamic, history-dependent cost environments, where evaluation costs vary with prior actions, such as travel distance in spatial tasks or edit distance in sequence design. LookaHES combines a multi-step variant of H-Entropy Search with pathwise sampling and neural policy optimization, enabling long-horizon planning beyond twenty steps without the exponential complexity of existing nonmyopic methods. The key innovation is the integration of neural policies, including large language models, to effectively navigate structured, combinatorial action spaces such as protein sequences. These policies amortize lookahead planning and can be integrated with domain-specific constraints during rollout. Empirically, LookaHES outperforms strong myopic and nonmyopic baselines across nine synthetic benchmarks from two to eight dimensions and two real-world tasks: geospatial optimization using NASA night-light imagery and protein sequence design with constrained token-level edits. In short, LookaHES provides a general, scalable, and cost-aware solution for robust long-horizon optimization in complex decision spaces, which makes it a useful tool for researchers in machine learning, statistics, and applied domains. Our implementation is available at https://github.com/sangttruong/nonmyopia.

Multimodality translation (e.g., text-to-image) is a core generative AI task. However, existing approaches (1) follow generative paths that do not directly represent the source modality, limiting the flexibility of some sampling algorithms; and (2) are unidirectional, preventing inversion (e.g., image-to-text). We propose BIT: Bidirectional Image-Text Diffusion Bridges. In contrast to previous approaches, BIT starts directly from text and interpolates into images, providing (1) a source-aware generative path that enables diverse and flexible sampling algorithms; and (2) an endpoint-conditioned process that can be traversed from image to text, providing a unified, bidirectional generative framework. BIT is derived through stochastic calculus, yielding SDE forms amenable to simulation and tractable loss functions that scale to high dimensions. Our experiments show that BIT is competitive with denoising-diffusion and deterministic-flow baselines, and outperforms them on several vision–language and natural-science evaluations.

Accurate and efficient discrete video tokenization is essential for long video sequences processing. Yet, the inherent complexity and variable information density of videos present a significant bottleneck for current tokenizers, which rigidly compress all content at a fixed rate, leading to redundancy or information loss. Drawing inspiration from Shannon's information theory, this paper introduces \alg, a principled framework for adaptive video tokenization. We rigorously prove that existing data-agnostic training methods are suboptimal in representation length, and present a novel evidence lower bound (ELBO)-based algorithm that approaches theoretical optimality. Leveraging this framework, we develop a transformer-based adaptive compressor that enables adaptive tokenization. Empirical results demonstrate state-of-the-art compression performance, saving $20\%$ tokens without influence on performance, and achieving $2.3\times$ compression rates while still outperforming prior heuristic adaptive approaches. By allocating tokens according to informational richness, \alg enables a more compressed yet accurate tokenization for video representation, offering valuable insights for future research.

Training-data attribution for vision generative models aims to identify which training data influenced a given output. While most methods score individual examples, practitioners often need group-level answers (e.g., artistic styles or object classes). Group-wise attribution is counterfactual: how would a model's behavior on a generated sample change if a group were absent from training? A natural realization of this counterfactual is Leave-One-Group-Out (LOGO) retraining, which retrains the model with each group removed; however, it becomes computationally prohibitive as the number of groups grows. We propose GUDA (Group Unlearning-based Data Attribution) for diffusion models, which approximates each counterfactual model by applying machine unlearning to a shared full-data model instead of training from scratch. GUDA quantifies group influence using differences in a likelihood-based scoring rule (ELBO) between the full model and each unlearned counterfactual. Experiments on CIFAR-10 and artistic style attribution with Stable Diffusion show that GUDA identifies primary contributing groups more reliably than semantic similarity, gradient-based attribution, and instance-level unlearning approaches, while achieving x100 speedup on CIFAR-10 over LOGO retraining.

Scientific discovery often requires many cycles of proposing, testing, and refining candidate solutions. Language models can increasingly participate in these loops, but simply generating more attempts does not ensure progress: parallel searches may duplicate one another and iterative refinement may become trapped in poor directions. The central challenge is therefore not only to scale AI-driven discovery, but to structure that scaling so that evaluation signals compound over time. Here we introduce SimpleTES (Simple Test-time Evaluation-driven Scaling), a framework that focuses on the structured scaling of AI discovery loops, organizing evaluator queries across independent trajectories, iterative refinement, local candidate selection, and the selective reuse of evaluated histories. Drawing on structural features of scientific communities, SimpleTES uses a single open-source GPT-OSS model to establish new state-of-the-art solutions across 28 open-ended problems in diverse scientific domains ranging from quantum physics and astronomy to biology, AI, and mathematics. These include a 24.5

Accurate and comprehensive measurement of household livelihoods is critical for monitoring progress towards poverty alleviation and targeting social assistance programs for those who most need it. However, the high cost of traditional data collection has historically made comprehensive measurement a difficult task in many locations. This paper evaluates alternative satellite-based deep learning approaches to local-level livelihoods measurement, using detailed and multi-year household census extracts from four African countries as training and evaluation data. We show that new machine-learning architectures based on transformers solve multiple open measurement problems, including high performance on measuring changes in livelihoods over time and accurate measurement of local-level variation in household asset wealth within cities, offering general improvement over previous benchmarks especially when training datasets are large. Experiments that artificially restrict data availability show that satellite-based models can make accurate predictions with limited training data. The proposed approach demonstrates the promise of combining satellite imagery and new deep learning architectures for hyperlocal and dynamic measurement of poverty in data-scarce environments.