We propose Schr\"odinger Bridge Mamba (SBM), a new concept of training-inference framework motivated by the inherent compatibility between Schr\"odinger Bridge (SB) training paradigm and selective state-space model Mamba. We exemplify the concept of SBM with an implementation for generative speech enhancement. Experiments on a joint denoising and dereverberation task using four benchmark datasets demonstrate that SBM, with only 1-step inference, outperforms strong baselines with 1-step or iterative inference and achieves the best real-time factor (RTF). Beyond speech enhancement, we discuss the integration of SB paradigm and selective state-space model architecture based on their underlying alignment, which indicates a promising direction for exploring new deep generative models potentially applicable to a broad range of generative tasks. Demo page: https://sbmse.github.io

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