In　the　federated　learning　scenario,　the　private　data　are　kept　local,　and　gradients　are　shared　to　train　the　global　model.　Because　gradients　are　updated　according　to　the　private　training　data,　the　features　of　the　data　are　encoded　into　gradients.　Prior　work　proved　the　possibility　of　reconstructing　the　private　training　data　based　on　gradients.　However,　only　a　small　batch　of　images　can　be　recovered,　and　the　reconstruction　quality,　especially　against　the　large　batch　size　of　images,　is　unsatisfactory.　To　improve　the　quality　of　reconstruction　of　a　large　batch　of　images,　a　generative　gradient　inversion　attack　based　on　a　regulation　term　is　designed,　which　is　called　fDLG.　First,　a　regulation　term　that　can　avoid　drastic　variations　within　image　regions　is　proposed,　which　is　based　on　the　cognition　that　changes　between　image　pixels　are　gradual.　The　proposed　regulation　term　encourages　the　synthesized　dummy　image　to　be　piece-wise　smooth.　Second,　generative　adversarial　networks　are　trained　to　improve　the　quality　of　the　attack　with　the　global　model　used　as　a　discriminator.　Simulation　shows　that　large　batches　of　images　(128　images　on　CIFAR100,　256　images　on　MNIST)　can　be　faithfully　reconstructed　at　high　resolution,　and　even　large　images　from　ImageNet　can　be　reconstructed.　©　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　London　Ltd.,　part　of　Springer　Nature　2024.