Optical diffraction tomography (ODT) offers high-resolution, label-free imaging of biological cells and clusters. This talk addresses reconstruction in ODT for a microscopic object undergoing a time-dependent smooth, but irregular motion induced by acoustic or optical forces. We establish a rigorous generalization of the Fourier diffraction theorem and derive efficient motion-aware reconstruction algorithms. Unknown motion of the object can be recovered by detecting common circles in the Fourier-transformed measurement data. The effectiveness of the algorithms is demonstrated on simulated and experimental data.