The authors introduce a multigrid training strategy to address the high computational costs and instability associated with modeling biochemical molecular systems at full resolution. This approach leverages low-resolution optimization to accelerate learning at higher resolutions by transferring parameters across different discretizations. For graph-based molecular representations, the method progressively transfers parameters from a coarse graph to increasingly finer graphs using biased random walk upsampling. In 3D molecular generation, structures are voxelized at multiple resolutions, allowing a coarse-resolution conditional Variational Autoencoder (CVAE) to be pretrained first. Shape-compatible convolutional parameters are then transferred from the coarse model to initialize a fine-resolution CVAE. Numerical experiments on receptor-conditioned 3D ligand generation demonstrate that this method accelerates convergence compared to training from scratch. Additionally, the study shows that multigrid training improves generalization capabilities for molecular generation tasks.