Normalizing Flows Across Dimensions
This addresses a bottleneck in generative modeling for structured data like images, offering an incremental improvement over existing flow architectures.
The paper tackles the problem that normalizing flows cannot learn low-dimensional data representations, introducing noisy injective flows (NIF) to map latent spaces to learnable manifolds with additive noise for deviations, resulting in significantly improved sample quality and separable data embeddings.
Real-world data with underlying structure, such as pictures of faces, are hypothesized to lie on a low-dimensional manifold. This manifold hypothesis has motivated state-of-the-art generative algorithms that learn low-dimensional data representations. Unfortunately, a popular generative model, normalizing flows, cannot take advantage of this. Normalizing flows are based on successive variable transformations that are, by design, incapable of learning lower-dimensional representations. In this paper we introduce noisy injective flows (NIF), a generalization of normalizing flows that can go across dimensions. NIF explicitly map the latent space to a learnable manifold in a high-dimensional data space using injective transformations. We further employ an additive noise model to account for deviations from the manifold and identify a stochastic inverse of the generative process. Empirically, we demonstrate that a simple application of our method to existing flow architectures can significantly improve sample quality and yield separable data embeddings.