Recent advancements in audio generation have been largely driven by Transformer-based diffusion models. However, these models suffer from quadratic complexity of self-attention, severely bottlenecking the long-form audio synthesis. To overcome this limitation, we propose MFlowAudio, a novel latent audio generation framework that synergizes the continuous-time dynamics of Flow Matching with a custom-designed TCMamba backbone. TCMamba uses an innovative dual-scan mechanism: a TimeMamba module to capture long-range causal dependencies with linear complexity, and a ChannelMamba module to model cross-channel correlations such as harmonic structures. Exploiting this structural foundation, we formulate the Stateful Flow Matching (SFM) paradigm. This framework inherently enables chunk-wise training and streaming generation, maintaining an $\mathcal{O}(1)$ caching complexity without incurring extra computational overhead. To enable fine-grained controllable synthesis, we devise a novel guidance mechanism that neutralizes vector field collisions precipitated by on-the-fly semantic transitions of prompts. Comprehensive empirical evaluations confirm that MFlowAudio yields generative fidelity on par with state-of-the-art baselines while establishing significant computational efficiency, achieving above $14.5$% acceleration in generation and facilitating perceptually seamless streaming synthesis with a constant latency of $1.8$ seconds. Demo: https://huggingface.co/spaces/mflowaudio/MFlowAudio

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