Supersampling Stable Diffusion and Beyond: Training-Free Neural Network Scaling via Signal Interpolation

Abstract

This work presents a training-free approach for interpolating neural networks using signal interpolation methods (i.e., linear, bilinear, bicubic). We discovered this phenomenon while attempting to interpolate the convolution layers of Stable-Diffusion-1.5 for beyond-training-resolution (BTR) image generation. As we know, for generating BTR images using DDPMs (Denoising Diffusion Probabilistic Models), there are mainly two approaches, namely, 1) patch-wise diffusion and 2) convolution-kernel dilation. Patch-wise diffusion cannot solve the object-duplication problem efficiently, while the kernel dilation approach may be harder to fine-tune later. Thus, we proposed convolution-kernel interpolation of the Stable Diffusion 1.5 model for $4\times$ BTR image generation. We discover and show mathematically that signal interpolation methods can correctly scale convolution kernels when multiplied by a flat-attenuation factor, while achieving competitive performance against the state of the art. We then applied the same methodology to non-DDPM deep neural network architectures, adapting them for BTR image classification, achieving a worst-case performance drop of $\sim 7\%$ on the ImageNet-1k validation set. Again, we subsample the penultimate fully connected layer of VGG-16 using our method, reducing up to $\sim 9\%$ parameters with $\sim 5\%$ loss in performance. Finally, we also discuss how we can reduce the memory footprint of training neural networks to $4\times$ or greater.