Ctrl-Z Sampling: Diffusion Sampling with Controlled Random Zigzag Explorations

Abstract: Diffusion models have shown strong performance in conditional generation by progressively denoising Gaussian noise toward a target data distribution. This denoising process can be interpreted as a form of hill climbing in a learned latent space, where the model iteratively refines the sample toward regions of higher probability. However, diffusion models often converge to local optima that are locally visually coherent yet globally inconsistent or conditionally misaligned, due to latent space complexity and suboptimal initialization. Prior efforts attempted to address this by strengthening guidance signals or manipulating the initial noise distribution. We introduce Controlled Random Zigzag Sampling (Ctrl-Z Sampling), a novel sampling strategy designed to detect and escape such local maxima during conditional generation. The method first identifies potential local maxima using a reward model. Upon detection, it injects noise and reverts to a previous, noisier state to escape the current optimization plateau. The reward model then evaluates candidate trajectories, accepting only those that offer improvement, while progressively deeper retreat enables stronger escapes when nearby alternatives fail. This controlled random zigzag process allows dynamic alternation between forward refinement and backward exploration, enhancing both alignment and visual quality in the generated outputs. The proposed Ctrl-Z Sampling is model-agnostic and compatible with existing diffusion frameworks. Experimental results show that Ctrl-Z Sampling substantially improves generation quality with only around 7.6X increase in function evaluations.