Linear combinations of Gaussian latents in generative models: interpolation and beyond

Sampling from generative models has become a crucial tool for applications like data synthesis and augmentation. Diffusion, Flow Matching and Continuous Normalizing Flows have shown effectiveness across various modalities, and rely on Gaussian latent variables for generation. For search-based or creative applications that require additional control over the generation process, it has become common to manipulate the latent variable directly. However, existing approaches for performing such manipulations (e.g. interpolation or forming low-dimensional representations) only work well in special cases or are network or data-modality specific. We propose Combination of Gaussian variables (COG) as a general purpose method to form linear combinations of latent variables while adhering to the assumptions of the generative model. COG is easy to implement yet outperforms recent sophisticated methods for interpolation. As COG naturally addresses the broader task of forming linear combinations, new capabilities are afforded, including the construction of subspaces of the latent space, dramatically simplifying the creation of expressive low-dimensional spaces of high-dimensional objects.