We present the starblade algorithm, a method to separate superimposed point sources from auto-correlated, diffuse flux using a Bayesian model. Point sources are assumed to be independent from each other and to follow a power-law brightness distribution. The diffuse emission is described as a non-parametric log-normal model with a priori unknown correlation structure. This model enforces positivity of the underlying emission and allows for variation in the order of magnitudes. The correlation structure is recovered non-parametrically in addition to the diffuse flux and is used for the separation of the point sources. Additionally many measurement artifacts appear as point-like or quasi-point-like effects, not compatible with superimposed diffuse emission. An estimate of the separation uncertainty can be provided as well. We demonstrate the capabilities of the derived method on synthetic data and data obtained by the Hubble Space Telescope, emphasizing its effect on instrumental artifacts as well as physical sources. The performance of this method is compared to the background estimation of the SExtractor method, as well as to a denoising auto-encoder.