CATCH: Counterfactual Anatomical Tissue Inpainting with Conditional Haar Diffusion

BraTS local synthesis replaces masked regions in T1-weighted brain MRI with plausible tumor-free tissue while preserving observed anatomy. We present CATCH, conditional 3D diffusion in an invertible Haar-wavelet domain. Its denoiser receives noisy target coefficients, voided-image coefficients, and a signed mask; tumor-excluded wavelet reconstruction and a hole-focused loss guide training, and hard compositing preserves observed voxels. We compare fixed masks, tumor-component augmentation, and a weighted mixture of tumor-derived, irregular-blob, and ellipsoidal masks. Of 25 development cases, five prespecified cases select each arm's checkpoint and all 25 of their trajectory aggregations; a separate 75-case internal set compares the frozen pipelines and selects a weighted mixture for organizer evaluation. Five-trajectory averaging yielded internal SSIM/PSNR/MSE (mean±SD) of 0.80±0.13, 19.18±1.80dB, and 0.010±0.005. As the sole officially evaluated pipeline, weighted mixture yielded 0.772±0.119, 20.89±3.27dB, and 0.0098±0.0054 on the 219-case BraTS 2026 validation set. Against compute-matched random augmentation internally, it improved SSIM by 0.019 (95% bootstrap CI: 0.013-0.025), PSNR by 0.95dB, and MSE by 0.003; all three paired comparisons remained significant after Holm correction. Results favor the complete weighted-mixture policy within CATCH; absent official fixed- and random-pipeline scores and a directly comparable external baseline limit broader conclusions.