In　compressed　sensing　applications,　self-learning　generative　models　have　attracted　increasing　attention　because　they　provide　guarantees　that　are　similar　to　those　of　standard　compressed　sensing　without　employing　sparsity.　However,　improving　the　performances　of　a　generative　model　is　challenging.　In　this　paper,　we　improve　the　recovery　performances　of　generative　models　(generative　adversarial　networks)　by　making　use　of　prior　knowledge　about　the　support　of　the　vector　of　the　original　signal　in　the　relevant　domain.　We　demonstrate　the　advantage　of　using　a　parametric　model　with　the　Fisher　distance　metric　for　the　exploitation　of　a　distribution　over　the　support　when　constraints　on　the　distribution　have　been　specified.　We　combine　the　generative　model　with　the　Fisher　distance　to　study　the　recovery　of　sparse　signals　that　satisfy　a　distribution　for　the　purpose　of　improving　the　recovery　performance　of　the　model　when　there　are　some　constraints　on　the　distribution.　Finally,　we　present　the　results　of　extensive　experiments　conducted　on　simulated　signals　and　imaging　signals.