Training-free camera control for pretrained flow-matching video generators is a partial-observation inverse problem: a depth-warped guidance video supplies noisy evidence on a subset of latent sites, which the sampler must reconcile with the pretrained prior. Existing methods struggle to balance the trade-off between trajectory adherence and visual quality and the heuristic guidance-strength tuning lacks robustness. We propose GibbsLens, which resolves this dilemma through a structural change to the sampler: each outer hard-replacement guidance step is augmented with an inner-loop block-conditional pseudo-Gibbs refinement on the unobserved complement at the same noise level, with provable convergence to the partial-observation conditional data law. To accelerate convergence on high-dimensional video latents, we exploit their conditional locality, partitioning the unobserved complement into 3D patches, each tracked by a custom mixing indicator that adaptively freezes converged patches. On RealEstate10K and DAVIS, GibbsLens attains the best FVD against all seven training-free and training-based competitors, outperforming every training-free baseline on every reported metric. Project page: https://xiye20.github.io/projects/GibbsLens/.
Many real-world problems, such as those with fairness constraints, involve complex expectation constraints and large datasets, necessitating the design of efficient stochastic methods to solve them. Most existing research focuses on cases with no {constraint} or easy-to-project constraints or deterministic constraints. In this paper, we consider nonconvex nonsmooth stochastic optimization problems with expectation constraints, for which we build a novel exact penalty model. We first show the relationship between the penalty model and the original problem. Then on solving the penalty problem, we present a single-loop SPIDER-type stochastic subgradient method, which utilizes the subgradients of both the objective and constraint functions, as well as the constraint function value at each iteration. Under certain regularity conditions (weaker than Slater-type constraint qualification or strong feasibility assumed in existing works), we establish an iteration complexity result of $O(ε^{-4})$ to reach a near-$ε$ stationary point of the penalized problem in expectation, matching the lower bound for such tasks. Building on the exact penalization, an $(ε,ε)$-KKT point of the original problem is obtained. For a few scenarios, our complexity of either the {objective} sample subgradient or the constraint sample function values can be lower than the state-of-the-art results by a factor of $ε^{-2}$. Moreover, on solving two fairness-constrained problems and a multi-class Neyman-Pearson classification problem, our method is significantly (up to 466 times) faster than the state-of-the-art algorithms, including switching subgradient method and inexact proximal point methods.