Robust synthesis of missing MRI modalities is essential for enabling the deployment of brain tumor segmentation pipelines in real-world clinical settings, where complete multi-modal scans are possibly unavailable due to acquisition constraints, scanner limitations, or patient-specific factors. This critical limitation is the focus of the Brain MR Image Synthesis Challenge (BraSyn), Task 8 of the BraTS-Lighthouse 2025 Challenge, which aims to foster generalizable and clinically deployable methods for synthesizing missing MRI modalities from available ones. To tackle this, we propose MISFIT – Modality Inference via Style Fusion and Invertible Translation – a novel two-stage generative framework for 3D brain MRI synthesis that operates entirely in the wavelet domain. MISFIT enhances the conditional wavelet diffusion paradigm by incorporating a Channel Attention Feature Fusion (CAFF) module for modality-aware representation learning and a Multi-Switchable SPADE block for style-conditioned generation. In Stage I, fused wavelet representations of the input modalities are used to generate a coarse approximation of the target modality. In Stage II, a denoising diffusion model - conditioned on both Stage I outputs and the original wavelet subbands - progressively reconstructs the final high-fidelity target volume. Evaluated on the BraSyn 2025 validation set, MISFIT achieves a PSNR of 18.65 dB and SSIM of 0.8041 in the randomized setting, demonstrating the viability of wavelet-based diffusion with adaptive fusion for medical image reconstruction. https://github.com/mohrsalt/MISFIT