We propose a novel two-stage framework for sensor depth enhancement, called Perfecting Depth. This framework leverages the stochastic nature of diffusion models to automatically detect unreliable depth regions while preserving geometric cues. In the first stage (stochastic estimation), the method identifies unreliable measurements and infers geometric structure by leveraging a training-inference domain gap. In the second stage (deterministic refinement), it enforces structural consistency and pixel-level accuracy using the uncertainty map derived from the first stage. By combining stochastic uncertainty modeling with deterministic refinement, our method yields dense, artifact-free depth maps with improved reliability. Experimental results demonstrate its effectiveness across diverse real-world scenarios. Furthermore, theoretical analysis, various experiments, and qualitative visualizations validate its robustness and scalability. Our framework sets a new baseline for sensor depth enhancement, with potential applications in autonomous driving, robotics, and immersive technologies.