-PD: Wavelet Phase Diffusion for Structurally and Semantically Consistent Sim-to-Real Translation

Simulation-to-reality translation must bridge the appearance gap between synthetic and real domains while preserving structural and semantic consistency. Conditioning-based methods achieve spatial alignment but introduce computationally expensive control modules. Meanwhile, paired-data methods achieve realism but rely on complex synthesis pipelines, often altering scene geometry and semantics. Training-free editing methods avoid both constraints but lack a learned appearance prior, limiting their perceptual quality. Recently proposed phase-preserving diffusion presents a promising alternative, but Fourier-domain formulations are constrained by global spectral coupling. This coupling induces spatial artifacts such as ringing and boundary leakage, thereby degrading structural and semantic consistency. We introduce Wavelet Phase Diffusion (-PD), which addresses this through two components. First, we operate in the Dual-Tree Complex Wavelet Packet Transform (DT-ℂWPT) domain, whose localized wavelet packets enable spatially adaptive phase injection without global spectral interference. Second, Low-Frequency Randomization (LFR) replaces the low-frequency packet, decoupling the model from the synthetic illumination prior and enabling in-distribution real-world appearance. Both components train on unpaired open-domain data, integrate into arbitrary diffusion backbones without architectural modification, and introduce negligible inference overhead. The spatial locality further enables region-selective translation, where chosen objects or areas can be turned realistic independently while the surrounding scene remains unchanged. On vKITTI → KITTI image translation, -PD outperforms prior methods in realism and semantic consistency while maintaining competitive structural alignment. For CARLA video translation, -PD approaches the realism of paired-data methods while reducing VLM planner ADE and FDE by 5.4% and 5.1%, respectively. It is the only evaluated method to jointly improve both appearance and downstream utility.