Papers › FInC Flow: Fast and Invertible k ×k Convolutions for Normalizing Flows
FInC Flow: Fast and Invertible k ×k Convolutions for Normalizing Flows
Aditya Kallappa, Sandeep Nagar, Girish Varma
Invertible convolutions have been an essential element for building expressive normalizing flow-based generative models since their introduction in Glow. Several attempts have been made to design invertible k ×k convolutions that are efficient in training and sampling passes. Though these attempts have improved the expressivity and sampling efficiency, they severely lagged behind Glow which used only 1 ×1 convolutions in terms of sampling time. Also, many of the approaches mask a large number of parameters of the underlying convolution, resulting in lower expressivity on a fixed run-time budget. We propose a k ×k convolutional layer and Deep Normalizing Flow architecture which i.) has a fast parallel inversion algorithm with running time O$(n k^2)$ (n is height and width of the input image and k is kernel size), ii.) masks the minimal amount of learnable parameters in a layer. iii.) gives better forward pass and sampling times comparable to other k ×k convolution-based models on real-world benchmarks. We provide an implementation of the proposed parallel algorithm for sampling using our invertible convolutions on GPUs. Benchmarks on CIFAR-10, ImageNet, and CelebA datasets show comparable performance to previous works regarding bits per dimension while significantly improving the sampling time.
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Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Image Generation | CelebA | FInCFlow | bpd (8-bits) | NaN | #1 of 1 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
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