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We introduce \textit{HALO} -- a deep generative model utilising HAmiltonianLatent Operators to reliably disentangle content and motion information inimage sequences. The \textit{content} represents summary statistics of asequence, and \textit{motion} is a dynamic process that determines howinformation is expressed in any part of the sequence. By modelling the dynamicsas a Hamiltonian motion, important desiderata are ensured: (1) the motion isreversible, (2) the symplectic, volume-preserving structure in phase spacemeans paths are continuous and are not divergent in the latent space.Consequently, the nearness of sequence frames is realised by the nearness oftheir coordinates in the phase space, which proves valuable for disentanglementand long-term sequence generation. The sequence space is generally comprised ofdifferent types of dynamical motions. To ensure long-term separability andallow controlled generation, we associate every motion with a uniqueHamiltonian that acts in its respective subspace. We demonstrate the utility of\textit{HALO} by swapping the motion of a pair of sequences, controlledgeneration, and image rotations.

Hamiltonian latent operators for content and motion disentanglement in image sequences