In recent years, there has been an increased interest in analyzing and generating the shape and motion of 3D humans (body and face). Advances in 3D human shape estimation algorithms, 3D scanning technology, hardware-accelerated 3D graphics, and related tools, are enabling access to large-scale 3D human body shape data. This data usually comes in the form of 3D surface meshes that, in general, do not correspond to coherent discretizations, i.e., the same surface can be represented by many different triangular meshes with varying connectivity and a varying number of vertices. Thus, methods designed for 3D/4D shape analysis of parameterized surfaces and deep learning face severe limitations when applied to such real data. Our goal is to generate a diverse set of plausible 3D human body and face motion dynamics directly from 3D scan data or even from a prompt space such as text or audio. The expected outcome of 4DSHAPE is to identify, develop and perfect a natural framework where one can both embed and generate surfaces of human body and faces independently of the way they are parameterized/discretized, including raw scans, in a way that captures and reproduces both the identity of the subject and the natural motions they can make. It is articulated around 3 main objectives: Objective 1: 3D-to-3D. Our first objective concerns the development of a discretization-invariant 3D-to-3D registration and reconstruction framework adapted to human body shapes based on a common latent space and auto-encoder model. Objective 2: 3D-to-4D. In the second objective we plan to investigate the extension of time-static (3D) to time-dynamic (4D) data. The central ingredient in this part of the research will be the construction of a non-linear structure on human shape latent space, which will enable us to accurately model the intricate nature of real life human body motions and deformations. Our approach will use a combination of data driven methods, and physically motivated, elastic deformation energies. Objective 3: prompt-to-3D/4D. In our third and final object we aim to learn a mapping from several prompt spaces to the space of human shapes; here the prompt space could be simply a text input space, but also a more complicated space such as voice recording, or even an animated human sketch.