Energyflow: A Physically Consistent Learning Framework for 3D Microscopy Deconvolution

Three-dimensional fluorescence microscopy images often suffer from blur and noise induced by the point spread function (PSF), leading to loss of resolution and structural fidelity. We propose EnergyFlow, a method for 3D microscopy deconvolution based on energy-guided flow matching. The model learns a restoration flow field along the continuous physical trajectory of degradation, while an energy consistency constraint enforces physical interpretability throughout the degradation-recovery process. This formulation enables image reconstruction without explicit inversion and achieves superior performance over classical deconvolution and deep learning baselines on both synthetic and real fluorescence data. The results demonstrate that energy-guided flow matching provides a robust and physically consistent framework for 3D microscopy restoration.