Understanding how cortical circuits encode sensory information remains a key challenge. Given a stimulus, the central question from the prespecitive of probablistic theories is how posterior probablities are neurally encoded. In recent years, standard approaches like sampling-based and variational approximations have been extended by deep neural networks (DNNs). For variational approaches, DNNs are frequently used to define encoders in variational autoencoders (VAE) settings. It remains unclear, however, what aspects of posterior approximations are important to explain neural encoding . Unlike most prior studies, we focus on models with discrete latent variables, which are well-suited for neural coding due to the binary nature of neural spiking, and which enable the application of novel encoding strategies. Concretely, we here apply two novel approaches: (A) amortized relaxed multivariate Bernoulli (ARMB), which enables DNN-based encoding for discrete latents; and (B) evolutionary variational optimization (EVO) that combines aspects of variational and sampling approximations. We test these approaches in the context of V1 simple cell coding using a linear generative model for natural image patches. ARMB applies a VAE-type encoding by modeling posterior mean as well as posterior correlations using DNN-based amortization; EVO can capture still richer posterior structure including multimodality and higher-order correlations. Both methods offer greater flexibility than VAE-type approaches, which conventionally do not go beyond means and variance modelling. Our analysis shows that both ARMB and EVO provide significant improvements compared to a baseline model, i.e., both result in higher marginal log-likelihoods. Simultaneously, the receptive fields (RFs) statistics predicted by the models becomes, with increasing likelihoods, increasingly similar to measurements in V1. The improvements using ARMB show the positive effect of encoding correlations. A stronger effect (for likelihood and RFs) is, however, observed for EVO which argues in favor of neural encodings being able capture posterior structure beyond pairwise correlations.