生成模型理论与方法

Longitudinal cohort studies produce repeated data that enable the assessment of time-varying association patterns between exposures and health outcomes. Classical linear mixed-effects models (LMMs) can accommodate a large variety of association patterns while accounting for the irregularly spaced, partially observed measurement. But they require the analyst to pre-specify the functional form linking the exposure history to the outcome. We propose the Neural ODE-LMM, which embeds a Neural Ordinary Differential Equation (Neural ODE) within the linear mixed-effects framework: a learned vector field encodes covariate trajectories into a continuous-time latent state that drives both the fixed- and random-effect design, while preserving the standard LMM observation model. This retains classical likelihood-based inference while learning complex, potentially cumulative, covariate effects flexibly. All parameters are estimated by maximising a penalised marginal likelihood. To quantify covariate effects, we introduce contrasts of counterfactual predictions that compare the expected outcome under alternative covariate trajectories with variance estimated via the delta method. In simulations, the model recovers both instantaneous and cumulative-burden effects without prior specification of the functional form. Applied to the Trois-Cités (3C) cohort, a population-based study of 7{,}324 participants, the method reveals trajectory-dependent associations of BMI and fasting glucose with cognitive decline.

Future wireless systems are expected to transform the surrounding space from a passive propagation medium into a smart electromagnetic environment, where engineered surfaces control wave propagation, support wireless sensing, and create programmable electromagnetic fingerprints. A key challenge in realizing this vision is the inverse design of metasurfaces for tailored electromagnetic propagation. While forward analysis evaluates the response of a known geometry, the inverse task starts from a prescribed scattering signature and seeks a physically realizable structure that produces it. This inverse task is inherently nonlinear and often high-dimensional, while candidate solutions may be non-unique and provide no direct indication of practical realizability. Here, we introduce a conditional diffusion framework for inverse design of dielectric resonator metasurfaces from target angular scattering patterns. Trained on T-matrix simulated geometry-response pairs, the model learns a conditional distribution of geometries instead of a deterministic mapping, enabling multiple candidate designs for the ill-posed inverse problem. The best generated metasurface achieves a mean percentage error of 1.39%, outperforming CMA-ES optimization (4.1% after 10 h) while requiring only about one minute for after-training inference. The model also produces lower error distributions than deterministic neural baselines for out-of-distribution spectra, highlighting the potential of diffusion models for efficient metasurface design.

We propose Discrete Diffusion Bridges (DDB), a novel framework designed to resolve the fundamental spatiotemporal misalignment of standard discrete diffusion in image translation and generation. By corrupting data into a pure mask state via a random schedule, the conventional forward process induces a twofold misalignment: spatially, this pure-mask destination entirely discards the rich structural priors of the source image; temporally, the random masking order inherently contradicts the ``easy-first, hard-last'' decoding mechanism used during inference. To address this, DDB constructs a direct and efficient trajectory between domains. Spatially, we introduce a hybrid absorption mechanism that redefines the absorbing state to a stochastic mixture of mask and source tokens, effectively injecting source prior as spatial anchors into the latent space. Temporally, we design an information-guided noise schedule that quantifies semantic variation to prioritize the corruption of high-information regions at earlier timesteps. This ensures the model learns to resolve difficult semantic changes using robust context from invariant regions. Extensive experiments validate the versatility and robustness of our framework across diverse generative paradigms. DDB effectively balances edit alignment with structural fidelity across both text-guided semantic manipulation and pure structural image translation, while inherently complementing text-to-image generation and guaranteeing robust high-quality decoding under extremely low sampling steps. Code and models are available at \href{https://github.com/HKU-HealthAI/DDB}{https://github.com/HKU-HealthAI/DDB}.

Text-to-spatial audio generation, such as text-to-First-Order Ambisonics (FOA), provides a convenient way to create spatial audio for billion-dollar gaming and film industries. However, existing text-to-FOA methods are largely data-driven and may produce audio that violates acoustic relations between source direction and distance. They also separate descriptive and parametric control, forcing users to trade usability for precision. In this paper, we present PhysWave, a physics-guided latent diffusion model for controllable text-to-FOA generation. PhysWave unifies natural-language and trajectory control through a shared waypoint-caption representation, and augments diffusion training with two differentiable acoustic priors: spherical-harmonic direction consistency and inverse-square distance consistency. To support dynamic spatial generation, we further construct a 300K-clip FOA dataset with diverse sound categories and source trajectories. Extensive results show that the proposed priors help PhysWave generate spatially consistent FOA audio while maintaining competitive audio quality. Further analyses show that these physics priors improve spatial consistency during training and can also be used as inference-time guidance for training-free spatial refinement.

To mitigate the time complexity of generative models, one-step generative models have recently emerged through direct mapping from noise to data in a single forward pass. However, the reward-guided fine-tuning method of one-step generative models remains largely unexplored. To address this, we consider one-step generators from an optimal transport view, investigating Wasserstein Gradient Flow (WGF) for modeling smooth and controlled distributional evolution in probability space. We then propose a novel reward-guided fine-tuning of a one-step generative model via WGF. We derive a practical training method that requires no reward gradients, thereby handling both non-differentiable and differentiable rewards. Moreover, our method provides smooth and stable reward-guided distributional updates while mitigating reward hacking and mode collapse. Experiments on 2D synthetic data, CIFAR-10, and ImageNet 256$\times$256 with diverse rewards, including JPEG (in)compressibility, class probability, Black-and-White and CLIP alignment, show that our method achieves better reward alignment compared to baselines.

Modern video generators routinely fail at physical dynamics: objects float, trajectories violate gravity, contacts vanish. Standard denoising and flow-matching objectives fit visual data distributions but do not explicitly penalize such physical violations. Existing remedies can improve physical consistency, but typically add substantial inference or training cost. Candidate-selection methods generate and score multiple videos, while gradient-based world-model guidance repeatedly decodes and re-encodes intermediate estimates. Generator-internal refinement adds perturbation and re-denoising loops, whereas post-training requires curated data and additional optimization. We propose Off-Manifold Refinement (OMR), an inference-time method that instead injects world-model feedback directly into a single sampling trajectory. During scheduled middle ODE steps, we augment the generator velocity with the gradient of an adapter-space V-JEPA 2.1 surprise energy. This external correction can move the latent away from the uncorrected sampling trajectory and toward regions ranked as more physically plausible by the frozen predictor, after which the generator continues rendering from the corrected state. A small trained latent-to-embedding adapter keeps the gradient tractable at inference, and both the video generator and the world model remain frozen. On our fixed 400-prompt VideoPhy-2 detailed subset, OMR lifts the joint Semantic-Adherence-and-Physical-Commonsense metric from 47.0% to 52.0% (+5.0pp absolute, +10.6% relative) over the base Wan2.2-T2V-A14B sampler. On a separate fixed 50-prompt efficiency subset, it requires $1.71 \times$ the base runtime rather than the multiplicative cost of reward/search alternatives. Project page: https://itruonghai.github.io/omr.

Diffusion models are increasingly used not only for sampling from learned data distributions, but also for generating samples that optimize task-specific objectives. A common approach is to guide the reverse diffusion process using gradients of an external objective. However, when the data distribution is supported on a structured feasible set, such as a manifold or a constraint set, gradient guidance can move samples away from the learned data geometry. In this paper, we study a simple projected-gradient-guided diffusion update based on the observation that the Stein denoising operator can act as an approximate projection onto the data geometry. The proposed update incorporates the objective gradient inside the denoising step, yielding an inference-time method that uses only a pretrained denoiser and gradient evaluations. We analyze this update as an inexact projected-gradient method for constrained optimization over learned feasible geometries. Our theory covers three settings: linear manifolds, compact convex feasible sets, and compact Riemannian submanifolds. In all these settings, we prove descent and finite-time convergence guarantees. Numerical experiments support the theoretical interpretation and illustrate how the proposed update balances objective descent with preservation of the learned geometry.

Large language models (LLMs) have shown promise for spatio-temporal forecasting, but existing approaches often rely on regularly sampled token sequences and struggle with irregular observations because of temporal asynchrony, representation-space misalignment, and limited context windows. We propose LLMODE, a token-efficient framework for irregular spatio-temporal forecasting with a frozen LLM backbone. LLMODE first uses a graph-aware ODE encoder to reconstruct irregular graph observations as a continuous-time latent trajectory. A Fixed-Budget Perceiver Resampler then compresses this variable-length trajectory into a fixed number of dynamic memory tokens. In parallel, compact statistical descriptors are encoded and resampled into context memory tokens. A dual-source gated cross-attention module injects both memories into the frozen LLM, enabling controlled utilization of external spatio-temporal evidence. Experiments on three real-world urban datasets and two physical-dynamics benchmarks show competitive overall performance, with clearer advantages under sparse or dynamically complex irregular sampling. Additional evaluations on unseen urban regions further demonstrate strong zero-shot generalization without adaptation.

3D Gaussian Splatting has achieved remarkable success in photorealistic rendering, yet it suffers from severe overfitting and geometric artifacts in sparse-view scenarios due to the inherent deficiency of photometric supervision. Recent advances have attempted to regularize optimization by incorporating external priors, such as depth, point clouds, or diffusion models. However, these methods typically overlook the non-uniform distribution of supervision across the viewing space, resulting in limited specificity in prior use and primitive control. In this paper, we propose GSPotential, a framework that quantifies view-space supervision imbalance using a Camera Potential Field. Our key insight is to identify supervision valleys where photometric constraints are most deficient, and use the potential field to guide reconstruction from two complementary aspects. First, we devise a probabilistic spherical sampling strategy that places informative virtual cameras in low-potential regions. Point-cloud renderings from these views then provide targeted geometric guidance. Second, the same field provides a directional coverage cue for conservative Gaussian updates in weakly covered spatial sectors. Extensive experiments demonstrate that GSPotential achieves high reconstruction fidelity while maintaining competitive training efficiency.

Natural images concentrate their detail in a small fraction of the frame, yet diffusion models spend a full token on every patch, in every layer and at every timestep. The waste is largest in pixel-space models, with no autoencoder to absorb low-level redundancy first. Probing a pretrained pixel text-to-image transformer, we find its middle-block tokens redundant wherever the image is flat. The redundancy occupies connected, content-shaped regions, and exploiting it requires tokens with the same geometry. Cutting a Hilbert ordering of the patches provides them. Consecutive positions are always image neighbours, so any contiguous run is a connected region whose size and shape follow the content, and grouping in two dimensions becomes a cut in one. Existing reductions each lose part of this. Similarity merging scatters its groups, latent bottlenecks discard position, and skipping deletes what it should summarize. We cut where the model's features change most and pool each run into one region token. Our Region Token Interface (\method{}) adapts a diffusion model to these tokens, with the region count drawn at random during fine-tuning so one checkpoint serves every budget. \method{} leads prior reduction methods at matched budgets, matches dense quality at $2.0\times$ the speed, and stays close at $2.6\times$. The code and models are open-sourced at https://eduardzamfir.github.io/rti

Joint-Embedding Predictive Architectures (JEPAs) have shown strong potential for learning compact predictive representations, and LeWorldModel (LeWM) extends this paradigm to reconstruction-free latent world modeling from pixels. However, its deterministic autoregressive predictor generates future states through repeated one-step transitions, which can accumulate errors and remain sensitive to task-irrelevant visual perturbations. In this work, we propose Flow-JEPA (F-JEPA), a conditional flow matching dynamics model that jointly generates a sequence of future latent states conditioned on the current observation and actions. A Gaussian distribution serves as the flow source, exposing the vector field to perturbed latent trajectories as it learns to transport them toward clean future representations. This formulation retains the reconstruction-free JEPA framework while replacing point-wise transition regression with stochastic trajectory-level prediction. F-JEPA raises mean success from $86%$ to $92%$ under clean observations and from $67%$ to $86%$ under noisy conditions, suggesting that conditional flow matching provides a promising alternative to deterministic autoregressive dynamics in JEPA world models.

Reference-guided stylization of scenes represented by 3D Gaussian Splatting (3DGS) is important for efficient and controllable 3D content creation. Existing VGG-feature-based 3D stylization methods provide stable rendered-view optimization, but often under-represent expressive reference style cues; diffusion models offer stronger image priors, yet direct per-view or score-based diffusion guidance can lead to view drift, local artifacts, and hard-to-control appearance updates. We present DReSG, a 3D-grounded residual-feedback framework for stylized Gaussian splatting. DReSG represents attention-guided diffusion proposals as residual targets relative to the current render, and progressively absorbs these residuals into a shared Gaussian scene through multi-view Gaussian feedback. To make this feedback stable and controllable, DReSG modulates residual strength during target construction and combines coverage-aware view selection with conflict-filtered color updates during multi-view fitting. Extensive experiments demonstrate that DReSG achieves competitive reference-guided stylization while better preserving scene structure and cross-view stability. Our project page is available at https://vpx-ecnu.github.io/DReSG-website/.

Recent video diffusion models have achieved remarkable generation quality, but high-fidelity results still largely depend on closed-source systems or costly large-scale infrastructure. Test-time scaling (TTS) offers a training-free way to improve lightweight generators by spending additional inference compute, yet existing methods mostly remain within a noise-search paradigm: they sample, select, or perturb denoising trajectories and discard low-scoring candidates after expensive generation. This generate-and-discard process wastes not only computation but also the partial motion, layout, or appearance structure already encoded in recoverable samples. We present GEARS (Guided Editing for Adaptive Recycling Search), a training-free framework that introduces {diagnosis-guided candidate recycling} into video TTS by turning such candidates into editable priors through a generation-evaluation-editing loop. GEARS consists of two collaborative components. The Stage-Aware Scheduler determines what to repair, when to repair it, and which candidates should be preserved, recycled, or discarded. The Candidate Recycler diagnoses recoverable failures from keyframes and multi-dimensional reward feedback, derives candidate-specific repair prompts, and repairs the corresponding candidates through manifold-aware latent SDEdit. The repaired candidates are recycled into the search pool, creating refinement paths beyond standard noise perturbation while preserving useful structure. Under matched NFE budgets, GEARS consistently outperforms existing video TTS methods on VBench, bringing a 1.3B model to a total score comparable to a 14B counterpart, and ablations verify the necessity of adaptive scheduling, diagnosis-conditioned editing, and manifold-aware re-denoising. Code is available on GitHub.

We aim to improve frozen flow-matching image generators by adding inference computation inside the denoiser, without changing model weights or the outer sampler. Existing generators usually spend extra test-time computation by increasing the number of sampling steps, which repeatedly evaluates the entire denoiser and couples quality gains to sampler cost. A key challenge is how to use extra computation inside a frozen transformer denoiser: the method must decide which tokens, layers, and sampling times receive repeated updates while preserving the original generation pipeline. We introduce a training-free looping framework that repeatedly applies selected transformer layers inside each denoising call. Dense and Sparse Token Loop vary the token scope; Sampling-Progress Gating and the loop layer range specify when and where looping is active; loop count and strength control the repeated updates; and Loop Guidance combines ordinary and looped vector-field predictions. Across two Scale-RAE model scales, loop variants improve primary and auxiliary quality metrics with competitive quality--efficiency trade-offs. Loop Guidance further improves both primary metrics across all three tested models; on Scale-RAE DiT2.4B, it raises GenEval from 0.4471 to 0.5691 and DPG-Bench from 0.7656 to 0.8053. Code will be released.

While modern generative models excel at modeling complex data, precise inference-time control in conditional generation remains a critical challenge. Classifier-free guidance (CFG) is a primary mechanism for such control, yet it is typically treated as a static tuning parameter. In flow-based models, however, the guidance scale fundamentally dictates the velocity field and the resulting probability path, making guidance selection a dynamic path-optimization problem. We introduce PathGuide, a framework that reformulates scalar CFG selection as an on-policy transport problem. Leveraging the weak form of the continuity equation, we derive a selection criterion with a direct path-correctness interpretation: we prove that if the guided field is weakly equivalent to the exact conditional field along the generated rollout, the sampler's path coincides with the target conditional law. For scalar CFG, this criterion yields a strictly quadratic local objective with an efficient, closed-form selector for each solver interval. PathGuide enables optimal guidance scales to be computed and used online during generation or fitted offline as a reusable piecewise-constant schedule. We validate our method on low-resolution image manifolds and controlled settings across various continuous-time flow constructions, demonstrating that this transport-based selector improves path alignment and sample fidelity over both fixed and state-of-the-art adaptive guidance baselines.

Image reconstruction for positron emission tomography (PET) is an ill-posed Poisson inverse problem that often suffers from severe noise amplification and artifacts. In this work, we introduce an unsupervised, optimization-based reconstruction framework that employs a flow-matching generative model as a learned manifold prior. We train the flow-matching model on high-quality PET images to learn a deterministic ordinary differential equation transport from a Gaussian latent distribution to the empirical PET image distribution, yielding a differentiable generator of anatomically plausible images. We incorporate this generator as an explicit manifold constraint into a regularized Poisson likelihood formulation. We solve the resulting optimization problem using an alternating direction method of multipliers algorithm, in which an expectation-maximization-type surrogate update enforces data consistency and a gradient-based latent-space projection enforces manifold proximity. We evaluate the proposed method on both simulated and real PET datasets, assessing dose-level robustness, lesion-insertion generalization, and cross-scanner transfer. Compared with conventional reconstruction methods and state-of-the-art deep learning baselines, the proposed method provides superior noise suppression, structural preservation, and quantitative accuracy, while maintaining high computational efficiency.

Diffusion-based visual generative models deliver strong image and video synthesis quality but incur high inference costs because sequential samplers repeatedly evaluate large networks. Caching-based methods reduce inference latency by reusing intermediate computations across adjacent timesteps. However, existing cache controllers rely primarily on local temporal variation and overlook the trajectory-level consequences of cache reuse. We introduce Error-Propagation-Aware Cache (EpaCache), a training-free caching policy that adaptively allocates the reuse budget on timesteps with lower downstream impact. Experiments on image and video synthesis models demonstrate that EpaCache consistently improves the latency--fidelity trade-off over existing caching methods. On FLUX.1-dev, EpaCache outperforms the prior state-of-the-art caching method in both latency and fidelity, reducing inference time from $11.7$ s to $11.3$ s while improving PSNR from $21.4$ to $22.8$. On HunyuanVideo, EpaCache achieves a $2.63\times$ speedup over uncached inference and improves SSIM from $0.891$ to $0.905$ over the prior state-of-the-art method at matched latency.

We establish quantitative convergence to the target and uniform-in-time propagation of chaos for Langevin-regularized Stein variational gradient descent. The Stein interaction need not be small relative to the confining Langevin drift and does not generally yield a contractive particle coupling. At the mean-field level, the Stein and Langevin components dissipate the same relative entropy in the kernel-induced Stein and $2$-Wasserstein geometries, producing the squared kernel Stein discrepancy and relative Fisher information. Under a log-Sobolev inequality for the target, this yields exponential last-iterate convergence. We also derive a finite-particle entropy identity relative to the product target, giving exponential-in-time convergence of the empirical measure up to polynomial sampling errors. For propagation of chaos, we develop two complementary finite-time approaches. A synchronous coupling, combined with exponential moment estimates for the nonlinear mean-field diffusion, yields explicit single-exponential bounds in Wasserstein distance and kernel Stein discrepancy (KSD). Moving-product entropy gives joint-law relative entropy control relative to the evolving mean-field product law and, through entropy superadditivity and concentration, fixed-marginal relative entropy and total variation bounds and empirical KSD estimates. Under an additional $T_2$ inequality for the initial law, it also yields Wasserstein bounds. Combining these finite-time estimates with target convergence at a logarithmic cutoff time gives polynomial uniform-in-time propagation of chaos rates in expectation for empirical KSD and $W_2^2$, and for fixed-marginal total variation and $W_2^2$. All bounds control the last iterate in physical time. We also compare the two finite-time mechanisms and identify regimes in which each gives the sharper polynomial exponent.

The ability to leverage images from co-available modalities to inform target-domain reconstruction is highly desirable in imaging algorithms. In this work, we introduce Generative Translation Priors (GTP)--a Bayesian framework that transforms diffusion-based image-to-image translation models into cross-modality image priors for ill-posed imaging inverse problems. GTP incorporates target-domain measurements through likelihood guidance, steering the translation process toward the desired posterior distribution. The framework is grounded in a theoretical analysis of the resulting posterior dynamics, which reveals an intrinsic bias introduced by likelihood guidance. We further characterize this bias and derive a ground-truth-free formulation for its estimation, enabling it to serve as a practical metric for assessing posterior sampling quality. Building on this analysis, we derive two discretized GTP algorithms based on gradient and proximal likelihood guidance, respectively. We validate GTP on computed tomography reconstruction with magnetic resonance side information, and on positron emission tomography reconstruction with computed tomography side information. Experiments demonstrate that GTP effectively incorporates complementary cross-modality information and achieves high-fidelity reconstruction even under severely undersampled measurements.

Representation learning begins when training changes the features that define similarity between data. A frozen-kernel model only reweights a fixed geometry. We establish quantum signal processing (QSP) as a solvable quantum model of the representation-learning regime. At arbitrary depth, we compute the exact mean and variance of its quantum neural tangent kernel, revealing an input-dependent angular geometry whose diagonal remains non-self-averaging even when the underlying unitary approaches Haar randomness. We also prove a sparse-data guarantee for the full nonlinear gradient flow without freezing or ensemble-averaging the kernel: the realized dynamics converges to an integrable scalar flow with a time-dependent kernel closure and explicit convergence times. A finite-depth speed limit holds for every data set and trajectory. At higher data density, numerical results show coupled evolution beyond both the scalar and frozen-kernel descriptions. These results give a controlled theory of learned quantum data geometry with provable training dynamics beyond the frozen limit.

Purpose: To develop and evaluate a diffusion-based reconstruction framework for highly accelerated 2D real-time (RT) cine cardiovascular magnetic resonance imaging (CMR). Methods: We trained an unconditional patch-based diffusion model and incorporated it into a reconstruction framework, termed CineDiff, using diffusion posterior sampling for data consistency. CineDiff was evaluated in four settings: (i) 30 retrospectively undersampled breath-held cine at 1.5T and 3T from healthy participants across multiple acceleration rates, (ii) 15 prospectively undersampled free-breathing RT cine at 1.5T and 3T from patients indicated for clinical CMR, and (iii) 10 prospectively undersampled mid-field (0.55T) free-breathing scans, including five from healthy subjects and five from porcine models. For retrospective undersampling, reconstruction quality was assessed using peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), learned perceptual image patch similarity (LPIPS), and deep image structure and texture similarity (DISTS). For prospective undersampling, image quality was evaluated by blinded expert scoring on a 5-point Likert scale. Results: In retrospectively undersampled breath-held cine data, CineDiff achieved higher PSNR and SSIM and lower LPIPS and DISTS than the comparison methods across all evaluated acceleration rates. In prospectively undersampled free-breathing RT cine data, CineDiff received higher expert image-quality scores. Qualitatively, CineDiff reduced block-like artifacts and preserved finer anatomical detail compared with traditional compressed sensing and a variational network method, termed CineVN. Conclusion: CineDiff enabled high-quality reconstruction of highly accelerated 2D RT cine CMR. The method also demonstrated robustness to out-of-distribution data, including mid-field and porcine acquisitions.

Large-scale diffusion models have fueled numerous profitable downstream applications for AI-related businesses, including visual editing and content creation. Meanwhile, due to the huge amount of resource consumption (e.g., computation and high-quality data) during training, such diffusion models are deemed valuable intellectual property (IP) for tech companies like OpenAI and Google. Yet, the IP assets are vulnerable to various unauthorized uses by adversaries seeking to steal models for customized, usually commercial applications. Some existing approaches have explored IP protection for AI models; however, they mostly face structural limitations in common --- using a training-time watermarking by injecting artifacts in the model, which can impose a measurable utility cost and can be weakened by post-hoc fine-tuning. To address these challenges, this work investigates IP protection (i.e., model ownership verification) for diffusion models in a realistic commercial scenario with minimal model utility loss. Specifically, the proposed method builds a framework for model ownership verification, termed ``{Membership is Ownership} (MiO)'', based on a population-level hypothesis test on a private member evidence dataset. MiO verifies ownership using two criteria: model attribution through membership inference and model separation from public references. Both are tested at $p<10^{-6}$. We evaluate MiO on DDIM and Stable Diffusion models without modifying the owner model or its sampling pipeline, and report ROC-AUC and true-positive rates at fixed nominal false-positive targets. Furthermore, MiO stays stable under different post-theft fine-tuning and weight perturbation in adversarial scenarios, reflecting better robustness compared to the watermarking methods.

Quantum federated learning enables collaborative model training across quantum devices without sharing raw data, and it faces the data and hardware heterogeneity inherent to noisy quantum devices. Utilizing the quantum geometric tensor is a natural remedy, yet pure-state approaches and diagonal approximations discard the correlations that encode parameter incompatibility. To address this, we extend the parameter-space geometry to the mixed states that noisy clients actually prepare. The real part of the resulting mixed-state geometric tensor is the Bures metric, which measures how fast the physical state changes under parameter variation, and the imaginary part is the mean Uhlmann curvature, which quantifies the incompatibility of estimating multiple parameters simultaneously. Accordingly, we employ the Bures metric as a local preconditioner and use the mean Uhlmann curvature to develop an achievable-precision aggregation rule that dynamically down-weights unreliable clients. Furthermore, we establish theoretical guarantees by proving a convergence theorem and a variance-dominance proposition. Empirical evaluations on a trapped-ion quantum emulator demonstrate that the proposed method maintains high accuracy across diverse device-heterogeneity conditions and outperforms standard federated averaging, whose accuracy degrades under strong noise.

This paper evaluates how reward function choice shapes the performance and behavior of LLM forecasters. We compare five proper scoring rules as training objectives for binary forecasts of resolved real-world events. Although the rules share the same theoretical incentive for truthful probability reporting, the resulting models differ in calibration, probability use, and estimated profiles of bias, information, and noise, with smaller differences in aggregate accuracy and discrimination. The Brier-trained model has the lowest observed Brier score and highest AUC-ROC, while the log-trained model has the highest observed log score and lowest calibration error. Models with similar aggregate performance also reach that performance through different combinations of bias, information, and noise. Proper scoring rules therefore need not behave interchangeably as training objectives. Reward choice may shape not only how well an LLM forecasts, but how its forecasting errors are structured. Each condition uses a single seed, so some differences may reflect training stochasticity.

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.

Recent generative approaches to geometry estimation adapt pretrained image diffusion models and treat the task as image-conditioned generation. Leveraging off-the-shelf image diffusion models, they either (i) train task-specific geometry models (for depth and surface normal estimation) independently, losing the opportunity of exploring the intrinsic correlation of these geometric targets, or (ii) jointly fine-tune modified image diffusion backbones (e.g., altered self-attention), which typically demands substantial labeled data. To overcome these limitations in a principled fashion, we repurpose pretrained video generative models as a unified and data-efficient framework for geometry estimation, formulated innovatively as a next-frames prediction task. Our method, GeoNeXt, inherits naturally structured knowledge and richer priors from the video model, while further adapting them for joint modeling of images and geometry targets (image <-> geometry), enabling more data efficient and effective learning of geometry. Extensive experiments validate our method for zero-shot monocular depth and surface normal estimation across diverse datasets, outperforming both previous task-specific and unified generative competitors while using substantially less training data. Notably, our method rivals discriminative state-of-the-art approaches trained on over 100x more data and even standouts on several benchmarks.

Flow matching enables likelihood-free training, yet alignment methods increasingly reuse conditional flow matching (CFM) losses as endpoint negative log-likelihoods (NLLs) and their old/new differences as log-likelihood ratios. We characterize when these substitutions are valid. For linear Gaussian paths, we exactly decompose endpoint NLL into entropy, a weighted CFM objective, an interior velocity--score residual, and a boundary residual. Thus CFM-only estimates and differences are exact only when the corresponding residuals cancel. At the off-policy population optimum, ordinary CFM is not generally a pointwise NLL estimator, whereas \(w_{\mathrm{sc}}(t)=(1-t)/t\) removes the interior residual; this positive result does not extend generally to training or on-policy alignment. On-policy log-ratios can remain biased even for identical endpoint laws or after surrogate optimization. Experiments across dimensions, distributions, and geometries support these conclusions and the mechanisms that make inexact ratios useful. **More broadly, the decomposition provides a theoretical basis for adapting likelihood-based LLM methods to flow matching, while distinguishing exact substitutions from controlled surrogates.**

Deep generative models have recently emerged as powerful priors for solving ill-posed inverse problems in CT, with diffusion-based approaches achieving state-of-the-art reconstruction performance. However, diffusion models typically rely on stochastic sampling procedures, long inference trajectories, and carefully tuned noise schedules, which can limit computational efficiency and numerical stability, especially at high spatial resolutions. In this work, we investigate Flow Matching as an alternative generative prior for CT reconstruction. We train a high-resolution Rectified Flow Matching model on 256x256 chest images from the Mayo Clinic Low-Dose CT dataset. To mitigate overfitting and limited anatomical variability, we employ a two-stage training strategy consisting of an initial phase with strong, anatomically informed data augmentation, followed by a fine-tuning phase with reduced or no augmentation to refine structural fidelity. The resulting model is capable of generating high-quality and anatomically coherent CT-like images, serving as a strong learned prior. We then evaluate multiple reconstruction methods specifically designed for Flow Matching models, including Plug-and-Play Flow, FlowDPS, Flower, and Flow-Priors (ICTM), and compare them against state-of-the-art diffusion-based reconstruction algorithms such as DDRM, DPS, and DiffPIR. Experimental results across several CT inverse problem settings show that Flow Matching-based approaches consistently outperform diffusion-based methods in terms of PSNR, SSIM, and perceptual quality, while requiring fewer sampling steps. Finally, we publicly release the trained Flow Matching model and accompanying code to facilitate reproducibility and future research. Overall, this work demonstrates that Flow Matching provides a stable, efficient, and effective alternative to diffusion models for high-resolution CT image reconstruction.

Deformable 3D Gaussian Splatting (D-3DGS) reconstructs dynamic scenes by deforming a canonical set of 3D Gaussians through a deformation field of frame time. Replacing its MLP with a stack of Closed-form Continuous-time (CfC) cells-a Liquid Neural Network that solves the Liquid Timeconstant ODE in closed form-gives the field continuous-time behaviour at feed-forward cost. That closed form, however, is only the deterministic limit of a noise-driven system, and drops the stochastic term usually credited for the robustness of liquid networks. We put it back: a small Gaussian perturbation is added to the time gate of every CfC cell, turning the deterministic field into a simple stochastic (SDE) one. The noise is used only during training, needs no solver, and reduces exactly to the CfC when switched off. On the synthetic D-NeRF scenes the stochastic field is on par with the deterministic CfC and beats the MLP baseline on most scenes; on the real-world NeRF-DS scenes the deterministic limit is already best and adding noise does not help. The study thus gives both a clean way to read the CfC field as an SDE and an honest account of when a plain noise term helps and when it does not.

A model's behavior on a task is jointly determined by the input it receives and the prior it brings in, i.e. the distribution over stimuli it implicitly expects. Interpretability research has traditionally studied models by holding inputs fixed and examining model responses either mechanistically, probing how internal structure represents inputs, or behaviorally, measuring how variation in inputs leads to variation in outputs. Neither reconstructs the prior distribution itself, since internal structure shows what a model can represent, not what it expects, and any fixed stimulus set leaves most of the possible input space unseen. In particular, such an input space in real-world settings, such as images seen by VLMs, is extremely high-dimensional and diverse. These priors thus remain a poorly understood component of models that nonetheless influence real-world behavior. We propose a method to sample from models' perceptual prior distributions directly, by steering a generative model to produce stimuli along controllable axes and running Gibbs sampling over that space with the model under study as the judge. We apply this to a variety of categories and target variables (such as trustworthiness in faces and cheapness in art images) and recover both canonical biases and surprising novel priors invisible to direct prompting, warranting further investigation of their downstream effects.