arXiv subjects

Stefano Ermon

Publications and source records attributed to Stefano Ermon.

At least 19 recordsLinked to original sources

arXiv2026

There and Back Again: Bidirectional Diffusion Bridges for Multimodality Translation

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.

cs.LG↗

arXiv2026

Constrained Decoding for Diffusion Language Models via Efficient Inference over Finite Automata

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% to 71.5%, and stochastic sampling accuracy from 22.3% to 69.0%, where the unconstrained baseline collapses, with under 5% wall-clock overhead.

cs.LG↗

arXiv2026

Diffusion Language Model Parallel Decoding via Product-of-Experts Bridge

Diffusion language models (DLMs) offer substantial speed advantages through parallel decoding, but the lack of token dependencies limits generation quality compared to autoregressive (AR) models. Recent progress attempts to bridge the gap via importance sampling, with DLM being the proposal and AR being the target. However, due to the huge gap between their distributions, the sampling requires a large number of particles and is thus expensive to compute. In this paper, we introduce PoE-Bridge, a novel decoding framework that drastically improves generation speed and accuracy by introducing an intermediate distribution to bridge the gap. The distribution is constructed as a Product-of-Experts (PoE) of the DLM proposal and the AR target. With the intermediate distribution, we first use the DLM to draft multiple continuations in parallel, then apply rejection sampling to verify the drafted tokens and move the resulting candidates toward the PoE. We then use importance sampling to further correct the PoE-aligned candidates toward the AR target. We further propose several improved techniques, including mixed-temperature sampling for enhanced diversity and elastic rejection windows for reducing wasted verification. Empirically, PoE-Bridge achieves significantly improved accuracy with $5\times$ speedup over the standard DLM decoding approach, and recovers at least 95% of the target AR model's performance, efficiently advancing most of the quality gap on challenging mathematical reasoning and coding tasks. Our code is available at https://github.com/juntongshi48/poe-bridge.

cs.CL↗

arXiv2026

Mitigating Bias in Locally Constrained Decoding via Tractable Proposals

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 $p_{\mathrm{lm}}( \cdot \mid \mathrm{constraint})$. 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.

cs.CL↗

arXiv2026

Beyond Pairwise Preferences: Listwise Reward-Aware Alignment for Diffusion Models

Preference optimization has emerged as an efficient alternative to online reinforcement learning from human feedback (RLHF) for aligning text-to-image diffusion models. However, existing methods largely reduce supervision to binary pairwise comparisons. This pairwise reduction is limiting when training data naturally contains multiple candidate images for the same prompt, and when continuous reward scores can provide richer information than a single winner-loser label. To address these limitations, we propose Diffusion LAIR, a reward-aware listwise preference optimization method for diffusion models. For each prompt, LAIR converts reward scores across a group of candidate images into centered advantage weights, then optimizes an advantage-weighted regression objective on the implicit reward, defined as the denoising-loss improvement of the current model over a fixed reference model, with a quadratic penalty that regularizes the magnitude of the implicit reward. The resulting objective uses all candidates simultaneously rather than selecting pairs, and remains conservative by explicitly controlling the magnitude of the implicit reward. The LAIR objective admits a bounded closed-form optimum in implicit-reward space, clarifying how the regularization strength controls the magnitude of the preference update. Experiments show that Diffusion LAIR outperforms strong preference optimization baselines on SD1.5 and SDXL across text-to-image generation, compositional generation, and image editing benchmarks.

cs.LG↗

arXiv2026

Can LLM Agents Respond to Disasters? Benchmarking Heterogeneous Geospatial Reasoning in Emergency Operations

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%, and alternative scaffolds yield at most a 3.24% gain; 3) compositional fragility scales with trajectory length, the agent-to-gold gap widening from 7% to 56% on long pipelines. DORA establishes a rigorous testbed for operationally reliable disaster-response agents.

cs.AI↗

arXiv2026

One-Step Generative Modeling via Wasserstein Gradient Flows

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$\times$256 generation, achieving 1.29 FID, with improved mode coverage and domain transfer. Compared to multi-step diffusion models with similar FID scores, our method yields approximately 100$\times$ faster sampling. These results show that Wasserstein gradient flows provide a principled and effective foundation for fast and high-fidelity generative modeling.

cs.LG↗

arXiv2026

Generative Modeling with Flux Matching

We introduce Flux Matching, a new paradigm for generative modeling that generalizes existing score-based models to a broader family of vector fields that need not be conservative. Rather than requiring the model to equal the data score, the Flux Matching objective imposes a weaker condition that admits infinitely many vector fields whose stationary distribution is the data. This flexibility enables a class of generative models that cannot be learned under score matching, in which inductive biases, structural priors, and properties of the dynamics can be directly imposed or optimized. We show that Flux Matching performs strongly on high-dimensional image datasets and, more importantly, that our added freedom unlocks a range of applications including faster sampling, interpretable and mechanistic models, and dynamics that encode directed dependencies between variables. More broadly, Flux Matching opens a new dimension in generative modeling by turning the vector field itself into a design choice rather than a fixed target. Code is available at https://github.com/peterpaohuang/flux_matching.

cs.LG↗

arXiv2026

ABC: Any-Subset Autoregression via Non-Markovian Diffusion Bridges in Continuous Time and Space

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.

cs.LG↗

arXiv2026

A satellite foundation model for improved wealth monitoring

Poverty statistics guide social policy, but in many low- and middle-income countries, censuses and household surveys that collect these data are costly, infrequent, quickly outdated, and sometimes error-prone. Satellite imagery offers global coverage and the possibility of predicting economic livelihoods at scale, yet existing approaches to predicting livelihoods with imagery or other non-traditional data often fail to reliably identify local-level variation and, as we show, degrade under temporal shift. Here we introduce Tempov, a satellite foundation model pretrained by self-supervision on three million bi-temporal Landsat pairs and adapted with parameter-efficient fine-tuning to sparse survey labels. The model enables large-scale, high-resolution wealth mapping and dynamic measurement, including zero-shot nowcasting up to a decade after observed labels, retrospective hindcasting, and decadal change tracking, while outperforming existing neural network and geospatial foundation-model baselines. In low-label regimes, Tempov achieves competitive accuracy with only 10% of survey samples, indicating substantially reduced dependence on expensive label collection. The model further generalizes across populous countries within and outside Africa, and scales to a unified Africa-wide model with strong continent-level performance ($R^2=0.63$, $r^2=0.68$), from which we generate high-resolution decadal maps of wealth and wealth changes for the African continent. Analysis of these maps shows large variation in recent economic performance both within and across countries. Our open-source approach provides a pathway to timely, scalable, low-cost monitoring of wealth and poverty from routinely collected satellite data.

cs.CY↗

arXiv2026

Structured Scaling of AI Discovery Across Diverse Scientific Domains

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% reduction in quantum circuit compilation overhead, up to 23% lower propulsive cost for deep-space trajectories, a 2.17x faster lasso-path solver, an 8.5% lower-error whole-brain neural-activity predictor, the fastest reported TriMul kernel, and new mathematical constructions beyond prior human or AI records. We further post-train the model for long-horizon discovery by assigning each attempt the final outcome of the trajectory it helped produce. This improves performance on both training and held-out mathematics problems, further advancing the frontier. Together, these results establish structured scaling as a general mechanism for advancing AI scientific discovery.

cs.LG↗

arXiv2026

Align Your Structures: Generating Trajectories with Structure Pretraining for Molecular Dynamics

Generating molecular dynamics (MD) trajectories using deep generative models has attracted increasing attention, yet remains inherently challenging due to the limited availability of MD data and the complexities involved in modeling high-dimensional MD distributions. To overcome these challenges, we propose a novel framework that leverages structure pretraining for MD trajectory generation. Specifically, we first train a diffusion-based structure generation model on a large-scale conformer dataset, on top of which we introduce an interpolator module trained on MD trajectory data, designed to enforce temporal consistency among generated structures. Our approach effectively harnesses abundant structural data to mitigate the scarcity of MD trajectory data and effectively decomposes the intricate MD modeling task into two manageable subproblems: structural generation and temporal alignment. We comprehensively evaluate our method on the QM9 and DRUGS small-molecule datasets across unconditional generation, forward simulation, and interpolation tasks, and further extend our framework and analysis to tetrapeptide and protein monomer systems. Experimental results confirm that our approach excels in generating chemically realistic MD trajectories, as evidenced by remarkable improvements of accuracy in geometric, dynamical, and energetic measurements.

cs.LG↗

arXiv2026

A Unified View of Score-Based and Drifting Models

Drifting models train one-step generators by optimizing a kernel-induced mean-shift discrepancy between the data and model distributions, with Laplace kernels used by default in practice. At each point, this discrepancy compares the kernel-weighted displacement toward nearby data samples with the corresponding displacement toward nearby model samples, thereby defining a transport direction for generated samples. In this paper, we show that drifting is more closely connected to score-based generative modeling than it may first appear, establishing a precise link to the score-matching principle underlying diffusion models. For Gaussian kernels, the population mean-shift field exactly equals the difference between the scores (i.e., the gradient-log-densities) of the Gaussian-smoothed data and model distributions. This identity follows from Tweedie's formula, which links the score of a Gaussian-smoothed density to its conditional mean, and implies that Gaussian-kernel drifting is exactly a score-matching objective on smoothed distributions. More generally, we derive an exact decomposition for radial kernels in which mean shift equals a score-based field plus a residual term. For the practical Laplace kernel, we further show theoretically and empirically that this residual is negligible in high dimension, implying that the transport field used in practice is nearly score-based. Our results reveal a structural connection to diffusion models: both methods use score-mismatch transport directions, but drifting realizes the score nonparametrically through kernel-based estimates, whereas diffusion models learn it parametrically with neural networks.

cs.LG↗

arXiv2026

Adaptive Spectral Feature Forecasting for Diffusion Sampling Acceleration

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$\times$ speedup on FLUX.1 and 4.67$\times$ speedup on Wan2.1-14B, while maintaining much higher sample quality compared with the baselines.

cs.CV↗

arXiv2026

Unpaired Image-to-Image Translation via a Self-Supervised Semantic Bridge

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.

cs.CV↗

arXiv2026

GUDA: Counterfactual Group-wise Training Data Attribution for Diffusion Models via Unlearning

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 ~100x speedup on CIFAR-10 over LOGO retraining.

cs.LG↗

arXiv2026

Improving Diffusion Language Model Decoding through Joint Search in Generation Order and Token Space

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%, 3.8%, 7.9%, and 6.8% absolute over backbone), matching or surpassing diffu-GRPO post-trained d1-LLaDA. Our work establishes joint search as a key component for advancing decoding in DLMs.

cs.CL↗

arXiv2026

Neural Nonmyopic Bayesian Optimization in Dynamic Cost Settings

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.

cs.LG↗