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arxiv: 2605.08698 · v2 · submitted 2026-05-09 · 💻 cs.CV · cs.LG

Recognition: no theorem link

Supersampling Stable Diffusion and Beyond: A Seamless, Training-Free Approach for Scaling Neural Networks Using Common Interpolation Methods

Md Abu Obaida Zishan , Jannatun Noor , Annajiat Alim Rasel
Authors on Pith no claims yet

Pith reviewed 2026-05-15 05:25 UTC · model grok-4.3

classification 💻 cs.CV cs.LG
keywords stable diffusionkernel interpolationhigher resolutiontraining-freeconvolution scalingneural network adaptationdiffusion modelsimage generation
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0 comments X

The pith

Interpolating scaled convolution kernels lets Stable Diffusion generate higher-resolution images without training.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that common interpolation methods applied to convolution kernels, when multiplied by a constant coefficient, correctly scale those kernels for higher input resolutions. This scaling property allows pre-trained Stable Diffusion models to produce images at resolutions larger than their training data without any fine-tuning or retraining. Empirically, the approach achieves competitive results compared to dilation methods while avoiding zero-gaps in kernels. It further extends to fully-connected layers, showing at most a 2.6 percent drop in accuracy when adapting networks to higher-dimensional data. The method also suggests ways to reduce training memory usage by a factor of four by training at lower resolutions and scaling up later.

Core claim

Interpolation of convolution kernels multiplied by a constant coefficient correctly scales the kernels, enabling zero-training higher-resolution image generation with Stable Diffusion models while achieving competitive empirical results. The same interpolation approach extends to fully-connected layers with a worst-case performance drop of 2.6% in accuracy and F1-score.

What carries the argument

Scaled kernel interpolation, which adjusts convolution weights to match new resolutions by interpolating and multiplying by a scaling factor.

If this is right

  • Stable Diffusion can generate images at arbitrary resolutions beyond training without retraining.
  • Object duplication artifacts are mitigated in higher-resolution outputs.
  • Performance on fully-connected networks drops by no more than 2.6% when interpolating for higher dimensions.
  • Training memory can be reduced up to 4 times by using lower-resolution training followed by kernel scaling.
  • Kernel interpolation provides a seamless alternative to dilation for scaling neural networks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This approach may enable on-the-fly resolution adaptation in deployed generative models.
  • Similar interpolation could be tested on transformer-based architectures for vision tasks.
  • Reducing training resolution and scaling kernels might lower computational costs for large-scale model development.

Load-bearing premise

That the scaled interpolated kernels will maintain the original model's learned behavior without introducing artifacts when applied to new resolutions or data distributions.

What would settle it

Generating images at twice the training resolution with the interpolated Stable Diffusion model and checking if object duplication or quality degradation occurs compared to standard methods.

Figures

Figures reproduced from arXiv: 2605.08698 by Annajiat Alim Rasel, Jannatun Noor, Md Abu Obaida Zishan.

Figure 1
Figure 1. Figure 1: Beyond-training-resolution generation using Stable Diffusion-1.5. A [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: UNet architecture of SD-1.5 for 512 × 512 image generation [17], [21] (the latent space is 8× downsampled by the first-stage model). Figure 2a shows the structure of each UNet block in Figure 2b. The dimensions shown below the block names in Figure 2b are input height and width dimensions for the respective block (channel dimensions are not shown). In Figure 2a, * denotes that the sub-block may or may not … view at source ↗
Figure 3
Figure 3. Figure 3: Training free methods for patch-wise diffusion for beyond-training-resolution image generation [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Training free methods for beyond-training-resolution image generation through dilating convolution [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: An overview of the interpolation and attenuation framework presented in this work. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of kernel interpolation methods. The figures on the left and right demonstrate spatial and [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Attenuated and interpolated version of Figures [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: UNet model architecture for denoising latents of the Stable Diffusion pipeline. The convolution sublayers [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: A castle is in the middle of a european city [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 9
Figure 9. Figure 9: A castle is in the middle of a european city [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: A nighstand topped with a white land-line phone, remote control, a metallic lamp, and a black hardcover [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 10
Figure 10. Figure 10: A nighstand topped with a white land-line phone, remote control, a metallic lamp, and a black hardcover [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: A painting of a koala wearing a princess dress and crown, with a confetti background. [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 11
Figure 11. Figure 11: A painting of a koala wearing a princess dress and crown, with a confetti background. [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: A professional photograph of an astronaut riding a horse [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
Figure 12
Figure 12. Figure 12: A professional photograph of an astronaut riding a horse [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: A teddy bear mad scientist mixing chemicals depicted in oil painting style [PITH_FULL_IMAGE:figures/full_fig_p025_13.png] view at source ↗
Figure 13
Figure 13. Figure 13: A teddy bear mad scientist mixing chemicals depicted in oil painting style [PITH_FULL_IMAGE:figures/full_fig_p024_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: A watercolor portrait of a woman by Luke Rueda Studios and David Downton. [PITH_FULL_IMAGE:figures/full_fig_p026_14.png] view at source ↗
Figure 14
Figure 14. Figure 14: A watercolor portrait of a woman by Luke Rueda Studios and David Downton. [PITH_FULL_IMAGE:figures/full_fig_p025_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Side-view blue-ice sneaker inspired by Spiderman created by Weta FX [PITH_FULL_IMAGE:figures/full_fig_p027_15.png] view at source ↗
Figure 15
Figure 15. Figure 15: Side-view blue-ice sneaker inspired by Spiderman created by Weta FX [PITH_FULL_IMAGE:figures/full_fig_p026_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Two cats, grey and black, are wearing steampunk attire and standing in front of a ship in a heavily detailed [PITH_FULL_IMAGE:figures/full_fig_p028_16.png] view at source ↗
Figure 16
Figure 16. Figure 16: Two cats, grey and black, are wearing steampunk attire and standing in front of a ship in a heavily detailed [PITH_FULL_IMAGE:figures/full_fig_p027_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Two little dogs looking a large pizza sitting on a table [PITH_FULL_IMAGE:figures/full_fig_p029_17.png] view at source ↗
Figure 17
Figure 17. Figure 17: Two little dogs looking a large pizza sitting on a table [PITH_FULL_IMAGE:figures/full_fig_p028_17.png] view at source ↗
read the original abstract

Stable Diffusion (SD) has evolved DDPM (Denoising Diffusion Probabilistic Model) based image generation significantly by denoising in latent space instead of feature space. This popularized DDPM-based image generation as the cost and compute barrier was significantly lowered. However, these models could only generate fixed-resolution images according to their training configuration. When we attempt to generate higher resolutions, the resulting images show object duplication artifacts consistently. To solve this problem without finetuning SD models, recent works have tried dilating the convolution kernels of the models and have achieved a great level of success. But dilated kernels are harder to fine-tune due to being zero-gapped. Apart from this, other methods, such as patched diffusion, could not solve the object-duplication problem efficiently. Hence, to overcome the limitations of dilated convolutions, we propose kernel interpolation of SD models for higher-resolution image generation. In this work, we show mathematically that interpolation can correctly scale convolution kernels if multiplied by a constant coefficient and achieve competitive empirical results in generating beyond-training-resolution images with Stable Diffusion using zero training. Furthermore, we demonstrate that our method enables interpolation of deep neural networks to adapt to higher-dimensional training data, with a worst-case performance drop of $2.6\%$ in accuracy and F1-Score relative to the baseline. This shows the applicability of our method to be general, where we interpolate fully-connected layers, going beyond convolution layers. We also discuss how we can reduce the memory footprints of training neural networks, using our method up to at least $4\times$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper claims that interpolating convolution kernels in Stable Diffusion (and extending to fully-connected layers) and multiplying by a constant coefficient mathematically scales the kernels to enable training-free higher-resolution image generation without object duplication artifacts, achieving competitive empirical results; it further claims this generalizes to higher-dimensional data with at most 2.6% drop in accuracy/F1 and can reduce training memory footprints by up to 4x.

Significance. If the scaling property is rigorously derived and holds for the full UNet (including non-convolutional components), the result would provide a simple, zero-cost supersampling technique for diffusion models and other networks, with practical value for memory-efficient training and resolution scaling in computer vision.

major comments (3)
  1. [Abstract] Abstract: the claim of a mathematical proof that interpolation plus a constant coefficient scales kernels correctly is asserted without any derivation steps, explicit constant value, or supporting equations; this is load-bearing for the central claim and must be supplied with full steps.
  2. [Method] Method (assumed §3): no explicit handling is described for sinusoidal time embeddings, MLP projections, or cross-attention layers in the Stable Diffusion UNet; leaving these at original scale while scaling only spatial convolutions risks inconsistent receptive fields and conditioning at higher resolutions.
  3. [Experiments] Experiments: empirical claims of 'competitive results' and 'at most 2.6% drop' rest on unspecified experiments with no quantitative tables, baselines (e.g., dilated kernels), or ablation on the constant coefficient; this prevents assessment of the zero-training assertion.
minor comments (1)
  1. [Abstract] Abstract: the memory-footprint reduction claim ('up to at least 4x') lacks any supporting calculation or experiment description.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and have revised the manuscript to strengthen the presentation of the mathematical derivation, clarify the scope of layer scaling, and expand the experimental details.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of a mathematical proof that interpolation plus a constant coefficient scales kernels correctly is asserted without any derivation steps, explicit constant value, or supporting equations; this is load-bearing for the central claim and must be supplied with full steps.

    Authors: We agree that the abstract should reference the key elements of the derivation. The full steps appear in Section 3: for a 2D convolution kernel of spatial support k, bilinear interpolation to resolution scale factor s followed by multiplication by s² preserves the total weight mass and the effective receptive field. We have updated the abstract to state the constant explicitly (s² for 2D, s³ for 3D) and to point to the derivation. revision: yes

  2. Referee: [Method] Method (assumed §3): no explicit handling is described for sinusoidal time embeddings, MLP projections, or cross-attention layers in the Stable Diffusion UNet; leaving these at original scale while scaling only spatial convolutions risks inconsistent receptive fields and conditioning at higher resolutions.

    Authors: Our approach scales only the spatial convolutional kernels because they alone determine the resolution-dependent receptive field. Time embeddings, MLP projections, and cross-attention operate on channel or token dimensions that remain unchanged with spatial upsampling; keeping them at native scale preserves the learned conditioning distribution. We have added a dedicated paragraph in the revised Method section justifying this design choice and reporting that conditioning quality (measured via CLIP score) remains comparable at higher resolutions. revision: partial

  3. Referee: [Experiments] Experiments: empirical claims of 'competitive results' and 'at most 2.6% drop' rest on unspecified experiments with no quantitative tables, baselines (e.g., dilated kernels), or ablation on the constant coefficient; this prevents assessment of the zero-training assertion.

    Authors: We have expanded the Experiments section with quantitative tables reporting FID, PSNR, and SSIM against both the native-resolution baseline and dilated-convolution baselines. An ablation on the constant coefficient is now included, showing that omitting the multiplier produces visible artifacts while the derived value yields the reported performance. The 2.6% worst-case drop is measured on MNIST/CIFAR-10 when interpolating fully-connected layers to higher input dimensions; all results use the zero-training protocol described in the paper. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper presents a mathematical demonstration that interpolating convolution kernels and multiplying by a constant coefficient scales them correctly for higher-resolution inference. This is framed as an independent first-principles property rather than a fit or redefinition of the target outputs. Empirical results on Stable Diffusion (zero-training competitive performance) and FC-layer interpolation (at most 2.6% drop) are reported separately as validation, not as inputs that define the scaling constant or force the outcome. No self-citations, uniqueness theorems, ansatzes smuggled via prior work, or renaming of known results appear in the load-bearing steps. The central claim therefore does not reduce to its own inputs by construction and remains externally falsifiable.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

The central claim rests on an unstated mathematical identity that interpolation of a kernel, after multiplication by a constant, equals the correctly scaled kernel for higher-resolution inputs. No free parameters beyond the constant coefficient are mentioned; no new entities are introduced.

free parameters (1)
  • constant coefficient
    The abstract states that kernels must be multiplied by a constant coefficient after interpolation; its value is not given and appears to be chosen to make the scaling identity hold.

pith-pipeline@v0.9.0 · 5598 in / 1301 out tokens · 27981 ms · 2026-05-15T05:25:40.438564+00:00 · methodology

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