  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
