MOTIVATION: The inference of cellular compositions from bulk and spatial transcriptomics data increasingly complements data analyses. Multiple computational approaches were suggested and recently, machine learning techniques were developed to systematically improve estimates. Such approaches allow to infer additional, less abundant cell types. However, they rely on training data which do not capture the full biological diversity encountered in transcriptomics analyses; data can contain cellular contributions not seen in the training data and as such, analyses can be biased or blurred. Thus, computational approaches have to deal with unknown, hidden contributions. Moreover, most methods are based on cellular archetypes which serve as a reference; e.g. a generic T-cell profile is used to infer the proportion of T-cells. It is well known that cells adapt their molecular phenotype to the environment and that pre-specified cell archetypes can distort the inference of cellular compositions. RESULTS: We propose Adaptive Digital Tissue Deconvolution (ADTD) to estimate cellular proportions of pre-selected cell types together with possibly unknown and hidden background contributions. Moreover, ADTD adapts prototypic reference profiles to the molecular environment of the cells, which further resolves cell-type specific gene regulation from bulk transcriptomics data. We verify this in simulation studies and demonstrate that ADTD improves existing approaches in estimating cellular compositions. In an application to bulk transcriptomics data from breast cancer patients, we demonstrate that ADTD provides insights into cell-type specific molecular differences between breast cancer subtypes. AVAILABILITY AND IMPLEMENTATION: A python implementation of ADTD and a tutorial are available at Gitlab and zenodo (doi:10.5281/zenodo.7548362).