Photometric redshift estimation algorithms are often based on representative data from observational campaigns. Data-driven methods of this type are subject to a number of potential deficiencies, such as sample bias and incompleteness. Motivated by these considerations, we propose using physically motivated synthetic spectral energy distributions in redshift estimation. In addition, the synthetic data would have to span a domain in colour-redshift space concordant with that of the targeted observational surveys. With a matched distribution and realistically modelled synthetic data in hand, a suitable regression algorithm can be appropriately trained; we use a mixture density network for this purpose. We also perform a zero-point recalibration to reduce the systematic differences between noise-free synthetic data and the (unavoidably) noisy observational data sets. This new redshift estimation framework, syth-z …