The organisation of the genome in nuclear space is an important frontier of biology. Chromosome conformation capture methods such as Hi-C and Micro-C produce genome-wide chromatin contact maps that provide rich data containing quantitative and qualitative information about genome architecture. Most conventional approaches to genome-wide chromosome conformation capture data are limited to the analysis of pre-defined features, and may therefore miss important biological information. One constraint is that biologically important features can be masked by high levels of technical noise in the data. Here we introduce a replicate-based method for deep learning from chromatin conformation contact maps. Using a Siamese network configuration our approach learns to distinguish technical noise from biological variation and outperforms image similarity metrics across a range of biological systems. The features extracted from Hi-C maps after perturbation of cohesin and CTCF reflect the distinct biological functions of cohesin and CTCF in the formation of domains and boundaries, respectively. The learnt distance metrics are biologically meaningful, as they mirror the density of cohesin and CTCF binding. These properties make our method a powerful tool for the exploration of chromosome conformation capture data, such as Hi-C capture Hi-C, and Micro-C.