Reconstructing high-quality point clouds from images remains challenging in computer vision. Existing generative models, particularly diffusion models, based approaches that directly learn the posterior may suffer from inflexibility--they require conditioning signals during training, support only a fixed number of input views, and need complete retraining for different measurements. Recent diffusion-based methods have attempted to address this by combining prior models with likelihood updates, but they rely on heuristic fixed step sizes for the likelihood update that lead to slow convergence and suboptimal reconstruction quality. We advance this line of approach by integrating our novel Forward Curvature-Matching (FCM) update method with diffusion sampling. Our method dynamically determines optimal step sizes using only forward automatic differentiation and finite-difference curvature estimates, enabling precise optimization of the likelihood update. This formulation enables high-fidelity reconstruction from both single-view and multi-view inputs, and supports various input modalities through simple operator substitution--all without retraining. Experiments on ShapeNet and CO3D datasets demonstrate that our method achieves superior reconstruction quality at matched or lower NFEs, yielding higher F-score and lower CD and EMD, validating its efficiency and adaptability for practical applications. Code is available at here.

Randomized-subspace methods reduce the cost of first-order optimization by using only low-dimensional projected-gradient information, a feature that is attractive in forward-mode automatic differentiation and communication-limited settings. While Nesterov acceleration is well understood for full-gradient and coordinate-based methods, obtaining accelerated methods for general subspace sketches that use only projected-gradient information and can improve over full-dimensional Nesterov acceleration in oracle complexity is technically nontrivial. We develop randomized-subspace Nesterov accelerated gradient methods for smooth convex and smooth strongly convex optimization under matrix smoothness and generic sketch moment assumptions. The key technical ingredient is a three-sequence formulation tailored to matrix smoothness, which recovers the corresponding classical Nesterov methods in the full-dimensional case. The resulting theory establishes accelerated oracle-complexity guarantees and makes explicit how matrix smoothness and the sketch distribution enter the complexity. It also provides a unified basis for comparing sketch families and identifying when randomized-subspace acceleration improves over full-dimensional Nesterov acceleration in oracle complexity.

Inthis section, we provide theoretical analysis ofHSPG. Moreover, we further point out that: (1) theSub-gradient Descent Stepwe used to achieve a "close enough" solution canbereplaced byothermethods, and(2)theAssumption 4isonlyasufficientcondition thatwecouldusetoshowthe"closeenough"condition. B.1 RelatedWork Problem (12)has been well studied indeterministic optimization with various algorithms that are capable ofreturning solutions with both lowobjectivevalueandhigh group sparsity under proper λ(95;73;42;64). For example, proximal stochastic variance-reduced gradient method (Prox-SVRG)(88)and proximal spider (Prox-Spider) (97) are developed to adopt multi-stage schemes based on the well-known variance reduction technique SVRG proposed in (46) and Spider developed in (22) respectively. Under Assumption 1, the search directiondk is a descent direction forψBk(xk), i.e., d>k ψBk(xk)<0.

Their method is a novel modification of Goldstein's classical subgradient method. Their work, however,makesuseofanonstandard subgradient oracle model andrequires the function to be directionally differentiable.