Understanding how cells respond to external stimuli is a central challenge in biomedical research and drug development. Current computational frameworks for modelling cellular responses remain restricted to two-dimensional representations, limiting their capacity to capture the complexity of cell morphology under perturbation. This dimensional constraint poses a critical bottleneck for the development of accurate virtual cell models. Here, we present FORM, a machine learning framework for predicting perturbation-induced changes in three-dimensional cellular structure. FORM consists of two components: a morphology encoder, trained end-to-end via a novel multi-channel VQGAN to learn compact 3D representations of cell shape, and a diffusion-based perturbation trajectory module that captures how morphology evolves across perturbation conditions. Trained on a large-scale dataset of over 65,000 multi-fluorescence 3D cell volumes spanning diverse chemical and genetic perturbations, FORM supports both unconditional morphology synthesis and conditional simulation of perturbed cell states. Beyond generation, FORM can predict downstream signalling activity, simulate combinatorial perturbation effects, and model morphodynamic transitions between states of unseen perturbations. To evaluate performance, we introduce MorphoEval, a benchmarking suite that quantifies perturbation-induced morphological changes in structural, statistical, and biological dimensions. Together, FORM and MorphoEval work toward the realisation of the 3D virtual cell by linking morphology, perturbation, and function through high-resolution predictive simulation.