Adaptive Weighted h-Transform Sampling for Coarse-Guided Visual Generation

Coarse-guided visual generation, which synthesizes fine visual samples from degraded or low-fidelity coarse references, is essential for various real-world applications. While training-based approaches are effective, they are inherently limited by high training costs and restricted generalization due to paired data collection. Accordingly, recent training-free works propose to leverage pretrained diffusion models and incorporate guidance during the sampling process. However, these training-free methods either require knowing the forward (fine-to-coarse) transformation operator, e.g., bicubic downsampling, or are difficult to balance between guidance and synthetic quality. To address these challenges, we propose a novel guided method by using the h-transform, a tool that can constrain stochastic processes (e.g., sampling process) under desired conditions. Specifically, we modify the transition probability at each sampling timestep by adding to the original differential equation with a drift function h, which approximately steers the generation toward the ideal fine sample. To address unavoidable approximation errors, we introduce an adaptive weight scheduler that combines a noise-level-aware initialization with a correction based on cross-timestep consistency, balancing guidance adherence and synthesis quality. Extensive experiments across diverse image and video generation tasks demonstrate its effectiveness and generalization.