Depth perception is fundamental for autonomous navigation, industrial inspection, and mixed-reality systems. It often operates under strict constraints on power and form factor. In such cases, monocular depth estimation (MDE) is often used. Even as recent advances continue to improve monocular depth quality, conventional frame-based MDE systems remain challenged by fast motion and high-dynamic-range scenes. This work introduces eSharp, an MDE framework that addresses these problems using an event camera. eSharp repurposes pretrained diffusion priors for event-only MDE and produces accurate metric depth with unparalleled sharpness on real data. Real-world event datasets provide only sparse LiDAR depth maps for ground-truth supervision, making dense prediction challenging. We address this limitation through cross-modal distillation, using LiDAR-calibrated dense pseudo-labels generated from a spatially co-registered frame camera to train eSharp. Experiments show that eSharp outperforms prior event-to-depth baselines in both metric-depth accuracy and spatial fidelity, establishing diffusion models as a promising foundation for event-driven 3D perception.
We consider the tensor principal components analysis (tensor PCA) problem on the sphere, in which we are asked to recover an unknown vector in $\mathcal{S}_N=\{x\in\mathbb{R}^N:\lVert x\rVert^2=N\}$ from a noisy observation of its $k$-th tensor power, for a fixed $k\ge3$. Tensor PCA exhibits a well-studied information-computation gap: global algorithms such as spectral methods and sum-of-squares work above an algorithmic threshold, below which we know matching lower bounds (against these and some other restricted models of computation). In contrast, local algorithms such as Markov chains were only known to succeed from a random initialization at a polynomially larger signal-to-noise ratio, and were believed to be inferior to global algorithms for tensor PCA. Continuing the program initiated in Part I [arXiv:2610.16705], we show that spherical Langevin dynamics, when supplemented with annealing and ergodic averaging, achieves polynomial-time strong recovery above the algorithmic threshold from a uniformly random initialization. Together with Part I, our results demonstrate that local Markov chains can succeed all the way down to the algorithmic threshold from an uninformative cold start.