Motivation: Shedding light on the relationships between protein sequences and functions is a challenging task with many implications in protein evolution, diseases understanding, and protein design. The protein sequence space mapping to specific functions is however hard to comprehend due to its complexity. Generative models help to decipher complex systems thanks to their abilities to learn and recreate data specificity. Applied to proteins, they can capture the sequence patterns associated with functions and point out important relationships between sequence positions. By learning these dependencies between sequences and functions, they can ultimately be used to generate new sequences and navigate through uncharted area of molecular evolution. Results: This study presents an Adversarial Auto-Encoder (AAE) approached, an unsupervised generative model, to generate new protein sequences. AAEs are tested on three protein families known for their multiple functions the sulfatase, the HUP and the TPP families. Clustering results on the encoded sequences from the latent space computed by AAEs display high level of homogeneity regarding the protein sequence functions. The study also reports and analyzes for the first time two sampling strategies based on latent space interpolation and latent space arithmetic to generate intermediate protein sequences sharing sequential properties of original sequences linked to known functional properties issued from different families and functions. Generated sequences by interpolation between latent space data points demonstrate the ability of the AAE to generalize and produce meaningful biological sequences from an evolutionary uncharted area of the biological sequence space. Finally, 3D structure models computed by comparative modelling using generated sequences and templates of different sub-families point out to the ability of the latent space arithmetic to successfully transfer protein sequence properties linked to function between different sub-families. All in all this study confirms the ability of deep learning frameworks to model biological complexity and bring new tools to explore amino acid sequence and functional spaces.