We propose a new method for separating superimposed sources using diffusion-based generative models. Our method relies only on separately trained statistical priors of independent sources to establish a new objective function guided by maximum a posteriori estimation with an $\alpha$-posterior, across multiple levels of Gaussian smoothing. Motivated by applications in radio-frequency (RF) systems, we are interested in sources with underlying discrete nature and the recovery of encoded bits from a signal of interest, as measured by the bit error rate (BER). Experimental results with RF mixtures demonstrate that our method results in a BER reduction of 95% over classical and existing learning-based methods. Our analysis demonstrates that our proposed method yields solutions that asymptotically approach the modes of an underlying discrete distribution. Furthermore, our method can be viewed as a multi-source extension to the recently proposed score distillation sampling scheme, shedding additional light on its use beyond conditional sampling. The project webpage is available at https://alpha-rgs.github.io

翻译：我们提出了一种利用扩散生成模型分离叠加源的新方法。该方法仅依赖于独立源的单独训练统计先验，通过在多个高斯平滑层级上建立基于最大后验估计与$\alpha$-后验的新目标函数。受射频系统应用启发，我们关注具有潜在离散性质的源，并从感兴趣信号中恢复编码比特，通过比特误码率（BER）进行评估。针对射频混合信号的实验结果表明，与经典及现有基于学习的方法相比，本方法的BER降低了95%。分析表明，所提方法能渐近逼近潜在离散分布的众数。此外，本方法可视为近期提出的分数蒸馏采样方案的多源扩展，为其在条件采样之外的应用提供了新见解。项目网页地址：https://alpha-rgs.github.io