In this paper, we formulate a novel image registration formalism dedicated to the estimation of unknown condition-related images, based on two or more known images and their associated conditions. We show how to practically model this formalism by using a new conditional U-Net architecture, which fully takes into account the conditional information and does not need any fixed image. Our formalism is then applied to image moving tumors for radiotherapy treatment at different breathing amplitude using 4D-CT (3D+t) scans in thoracoabdominal regions. This driving application is particularly complex as it requires to stitch a collection of sequential 2D slices into several 3D volumes at different organ positions. Movement interpolation with standard methods then generates well known reconstruction artefacts in the assembled volumes due to irregular patient breathing, hysteresis and poor correlation of breathing signal to internal motion. Results obtained on 4D-CT clinical data showcase artefact-free volumes achieved through real-time latencies. The code is publicly available at https://github.com/Kheil-Z/IMITATE .