arXiv:2610.22910v1 Announce Type: new Abstract: Speech bandwidth extension (BWE) aims to recover missing spectral content from band-limited speech. However, most generative BWE methods are designed for fixed input bandwidths and rely on iterative sampling, limiting their flexibility and efficiency. We propose BDR-BWE, a three-stage generative framework for multi-bandwidth speech extension. First, to enable conditional generation from the observed band-limited spectrum, we design a cutoff-aware conditional flow bridge in the compressed complex STFT domain, focusing generation on the missing high-frequency band while preserving observed spectral information. Second, progressive consistency distillation compresses the multi-step flow transport into a one-step generator. Third, adversarial refinement further improves high-frequency detail and harmonic coherence. BDR-BWE achieves state-of-the-art log-spectral distance (LSD) on VCTK across all evaluated bandwidths with one-step inference, while maintaining competitive perceptual quality and generalizing well to EARS. Audio samples are available at https://aizhiqi-work.github.io/bdr-bwe-demo.