Linear combinations of latents in generative models: subspaces and beyond

This repository provides an implementation of LOL (Linear combinations Of Latent variables), as presented in the paper:

Linear Combinations of Latents in Generative Models: Subspaces and Beyond

Abstract

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 latent variables for generation. For experimental design or creative applications that require more 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 Linear combinations of Latent variables (LOL) as a general-purpose method to form linear combinations of latent variables that adhere to the assumptions of the generative model. As LOL is easy to implement and naturally addresses the broader task of forming any linear combinations, e.g. the construction of subspaces of the latent space, LOL dramatically simplifies the creation of expressive low-dimensional representations of high-dimensional objects.

Usage

To see the LOL method in use, please see the provided example notebooks:

• example_interpolation.ipynb – Demonstrates simple interpolation.
• example_subspace.ipynb – Illustrates how latent subspaces can be defined.
• example_grid.ipynb – Similar as above but directly using linear combination weights.

from lolatents.lol_numpy import lol_iid
# from lolatents.lol_torch import lol_iid # for PyTorch

latents = lol_iid(
  w=w_grid_including_remaining,
  X=seed_latents,
  cdf=latent_distribution.cdf,
  inverse_cdf=latent_distribution.ppf
)

Installation

To use this repository, clone it and install dependencies:

git clone https://github.com/bodin-e/linear-combinations-of-latents.git
cd linear-combinations-of-latents
pip install -r requirements.txt