Diffusion models have achieved remarkable progress in universal image restoration. However, existing methods perform naive inference in the reverse process, which leads to cumulative errors under limited sampling steps and large step intervals. Moreover, they struggle to balance the commonality of degradation representations with restoration quality, often depending on complex compensation mechanisms that enhance fidelity at the expense of efficiency. To address these challenges, we introduce DGSolver, a diffusion generalist solver with universal posterior sampling. We first derive the exact ordinary differential equations for generalist diffusion models to unify degradation representations and design tailored high-order solvers with a queue-based accelerated sampling strategy to improve both accuracy and efficiency. We then integrate universal posterior sampling to better approximate manifold-constrained gradients, yielding a more accurate noise estimation and correcting errors in inverse inference. Extensive experiments demonstrate that DGSolver outperforms state-of-the-art methods in restoration accuracy, stability, and scalability, both qualitatively and quantitatively.

Diffusion models (DMs) excel in image generation but suffer from slow inference and training-inference discrepancies. Although gradient-based solvers for DMs accelerate denoising inference, they often lack theoretical foundations in information transmission efficiency. In this work, we introduce an information-theoretic perspective on the inference processes of DMs, revealing that successful denoising fundamentally reduces conditional entropy in reverse transitions. This principle leads to our key insights into the inference processes: (1) data prediction parameterization outperforms its noise counterpart, and (2) optimizing conditional variance offers a reference-free way to minimize both transition and reconstruction errors. Based on these insights, we propose an entropy-aware variance optimized method for the generative process of DMs, called EVODiff, which systematically reduces uncertainty by optimizing conditional entropy during denoising. Extensive experiments on DMs validate our insights and demonstrate that our method significantly and consistently outperforms state-of-the-art (SOTA) gradient-based solvers. For example, compared to the DPM-Solver++, EVODiff reduces the reconstruction error by up to 45.5% (FID improves from 5.10 to 2.78) at 10 function evaluations (NFE) on CIFAR-10, cuts the NFE cost by 25% (from 20 to 15 NFE) for highquality samples on ImageNet-256, and improves text-to-image generation while reducing artifacts.

Text-to-image (T2I) diffusion/flow models have drawn considerable attention recently due to their remarkable ability to deliver flexible visual creations. Still, high-resolution image synthesis presents formidable challenges due to the scarcity and complexity of high-resolution content. Recent approaches have investigated training-free strategies to enable high-resolution image synthesis with pre-trained models. However, these techniques often struggle with generating high-quality visuals and tend to exhibit artifacts or low-fidelity details, as they typically rely solely on the endpoint of the low-resolution sampling trajectory while neglecting intermediate states that are critical for preserving structure and synthesizing finer detail. To this end, we present HiFlow, a training-free and model-agnostic framework to unlock the resolution potential of pre-trained flow models. Specifically, HiFlow establishes a virtual reference flow within the high-resolution space that effectively captures the characteristics of low-resolution flow information, offering guidance for high-resolution generation through three key aspects: initialization alignment for low-frequency consistency, direction alignment for structure preservation, and acceleration alignment for detail fidelity. By leveraging such flow-aligned guidance, HiFlow substantially elevates the quality of high-resolution image synthesis of T2I models and demonstrates versatility across their personalized variants.

Adaptive beamforming is a cornerstone of array signal processing, yet its performance often collapses in the face of complex, rapidly changing interference. When interferers appear or move unpredictably, conventional estimators encounter a fundamental memory trade-off: short windows enable rapid tracking but suffer from high estimation variance, while long windows provide stable rejection but fail to adapt to shifts. This challenge is resolved by introducing the Universal Switching Beamformer (USB), which integrates competitive sequential prediction into the beamforming architecture. By employing a linear transition diagram, the USB implicitly maintains an exponentially large family of candidate covariance histories and dynamically re-weights them based on their cumulative output power. This mechanism allows the beamformer to automatically vary its effective memory length without explicit change detection or heuristic parameter tuning. A theoretical upper bound is proven on the regret relative to an omniscient oracle that selects the best piecewise-stationary covariance model in hindsight. Extensive simulations and experiments on the SwellEx-96 dataset demonstrate that the USB achieves the agility of short-window estimators and the precision of long-term integration, providing a principled solution for tracking highly non-stationary scenes.

The Volterra signature extends the classical path signature by incorporating general matrix-valued kernel into its iterated integral structure, yielding a flexible notion of memory for time series. Its components can be viewed as successive Picard iterates of linear controlled Volterra equations, making their exact computation of additional mathematical interest. However, the kernel introduces substantial algorithmic challenges. We provide a resolution by first decomposing the Chen-type convolution relation established in [13] into analytic and arithmetic parts, and then introducing several efficient algorithms: a general approximative scheme with quadratic complexity O(J2) in the number of time steps J, an FFT-based acceleration with complexity O(J logJ) for convolution kernels on uniform grids, and an exact recursion with complexity O(JR2) for kernels admitting a state-space representation of dimension R; retaining standard signature complexity in the path dimension and truncation level N. We further show that the number of factors in matrix-valued kernels of the form K(t,s) = P p kp(t s)Ap do not increase the asymptotic complexity in J and N. Finally, we derive a finite-difference predictor-corrector scheme for the associated Volterra signature kernel. All algorithms are implemented in the publicly available JAX-based package tensordev.

In this paper, we consider the problem of black-box optimization with noisy feedback revealed in batches, where the unknown function to optimize has a bounded norm in some Reproducing Kernel Hilbert Space (RKHS). We refer to this as the Batched Kernelized Bandits problem, and refine and extend existing results on regret bounds. For algorithmic upper bounds, (Li and Scarlett, 2022) shows that $B=O(\log\log T)$ batches suffice to attain near-optimal regret, where $T$ is the time horizon and $B$ is the number of batches. We further refine this by (i) finding the optimal number of batches including constant factors (to within $1+o(1)$), and (ii) removing a factor of $B$ in the regret bound. For algorithm-independent lower bounds, noticing that existing results only apply when the batch sizes are fixed in advance, we present novel lower bounds when the batch sizes are chosen adaptively, and show that adaptive batches have essentially same minimax regret scaling as fixed batches. Furthermore, we consider a robust setting where the goal is to choose points for which the function value remains high even after an adversarial perturbation. We present the robust-BPE algorithm, and show that a suitably-defined cumulative regret notion incurs the same bound as the non-robust setting, and derive a simple regret bound significantly below that of previous work.

In particular, GenRec achieves competitive recognition performance, offering 75.8% and 87.2% accuracy on SSV2andK400,respectively.

Indeed, this is a central question of recent workstudyinggeneralized lowrankmodels.

FromTheorem 2,thevariational gap is strictly positive as long as the rotation part of the score network remainstobenonzero.