Schematic of MADNESS workflow. The algorithm takes as input a field of galaxies and their detected positions. The VAE-deblender consisting of convolutional and dense layers initializes the latent space (Z), which is followed by the optimization of the sum of the log-prior and the log-likelihood by using the decoder (dense and transposed convolutional layers) to map latent space representations to the image space and the normalizing flow which uses MAF layers to compute the log-prior. Once the stopping condition is satisfied based on the rate of decrease of the minimization objective, we obtain the maximum a posteriori solution Z^* as output. The corresponding image space solutions can be found with a forward pass through the decoder.