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We propose a new method for separating superimposed sources usingdiffusion-based generative models. Our method relies only on separately trainedstatistical priors of independent sources to establish a new objective functionguided by maximum a posteriori estimation with an $\alpha$-posterior, acrossmultiple levels of Gaussian smoothing. Motivated by applications inradio-frequency (RF) systems, we are interested in sources with underlyingdiscrete nature and the recovery of encoded bits from a signal of interest, asmeasured by the bit error rate (BER). Experimental results with RF mixturesdemonstrate that our method results in a BER reduction of 95% over classicaland existing learning-based methods. Our analysis demonstrates that ourproposed method yields solutions that asymptotically approach the modes of anunderlying discrete distribution. Furthermore, our method can be viewed as amulti-source extension to the recently proposed score distillation samplingscheme, shedding additional light on its use beyond conditional sampling. Theproject webpage is available at https://alpha-rgs.github.io

Score-based Source Separation with Applications to Digital Communication Signals