Single Image Super-Resolution via Bivariate `A Trous Wavelet Diffusion

Maryam Heidari; Nantheera Anantrasirichai; Alin Achim

cs.CVMar 7, 2026

Single Image Super-Resolution via Bivariate `A Trous Wavelet Diffusion

Authors: Maryam Heidari, Nantheera Anantrasirichai, Alin Achim

Organizations: Visual Information Laboratory, University of Bristol, Bristol, UK

Abstract

The effectiveness of super resolution (SR) models hinges on their ability to recover high frequency structure without introducing artifacts. Diffusion based approaches have recently advanced the state of the art in SR. However, most diffusion based SR pipelines operate purely in the spatial domain, which may yield high frequency details that are not well supported by the underlying low resolution evidence. On the other hand, unlike supervised SR models that may inject dataset specific textures, single image SR relies primarily on internal image statistics and can therefore be less prone to dataset-driven hallucinations; nevertheless, ambiguity in the LR observation can still lead to inconsistent high frequency details. To tackle this problem, we introduce BATDiff, an unsupervised Bivariate A trous Wavelet Diffusion model designed to provide structured cross scale guidance during the generative process. BATDiff employs an a Trous wavelet transform that constructs an undecimated multiscale representation in which high frequency components are progressively revealed while the full spatial resolution is preserved. As the core inference mechanism, BATDiff includes a bivariate cross scale module that models parent child dependencies between adjacent scales. It improves high frequency coherence and reduces mismatch artifacts in diffusion based SR. Experiments on standard benchmarks demonstrate that BATDiff produces sharper and more structurally consistent reconstructions than existing diffusion and non diffusion baselines, achieving improvements in fidelity and perceptual quality.

Figures & tables

Figure 1: Overview of BATDiff. Given an observed LR image $y$ , we form an HR-grid reference $x_{\mathrm{ref}}=\mathcal{U}(y)$ via bicubic upsampling and build an undecimated à trous pyramid $\mathcal{A}$ to obtain multiscale wavelet planes $\{w^{(s)}\}$ ( S =6). We construct progressively refined clean targets $\{x^{(s)}_{0}\}$ (Eq. ( 6 )) and train a shared DDPM by forward noising at each scale. At inference, reverse diffusion proceeds from coarse to fine with bivariate denoising conditioned on the time-aligned parent state $x^{(s-1)}_{t}$ , followed by an LR-consistency correction $\mathcal{P}_{y}$ after each step.

Dataset	Method	Sup.	Training dataset	PSNR $\uparrow$	SSIM $\uparrow$
DIV2K	EDSR [ 26 ]	P	DF2K	28.98	0.83
	BSRGAN [ 51 ]	P	DIV2K+Flickr2K+WED+FFHQ	22.56	0.7352
	SRDiff [ 21 ]	P	DIV2K	27.41	0.79
	DiWa [ 29 ]	P	DIV2K	28.09	0.78
	FDDiff [ 42 ]	P	DIV2K	27.53	0.85
	StableSR [ 41 ]	P	DIV2K+DIV8K+Flickr2K+OST	20.59	0.6562

Table 1: Quantitative comparison on standard SR benchmarks with an up-sampling scale of

\times 4

. P : paired, U : unpaired, SI : single-image. Best/second-best within each comparable block are bold / underlined .

Dataset	MetaSR [ 13 ]	LIIF [ 7 ]	LTE [ 19 ]	CLIT [ 6 ]	CiaoSR [ 4 ]	HIIF [ 15 ]	Ours $\times 8$
Set5	27.02	27.36	27.35	27.62	27.45	27.56	28.74
Set14	25.09	25.34	25.42	25.55	25.42	25.59	27.12
Urban100	22.75	23.14	23.17	23.33	23.34	23.36	23.47

Table 2: Quantitative comparison (PSNR

\uparrow

) on standard SR benchmarks with an up-sampling scale of

\times 8

). Best/second-best within each comparable block are bold / underlined .

Figure 2: Qualitative comparison on standard SR benchmarks ( $\times 4$ ).

LR-cons.	À trous	Bivariate	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
✓	✗	✗	26.93	0.8240	0.1784
✓	✓	✗	27.46	0.8377	0.1723
✓	✓	✓	28.53	0.8502	0.1647

Table 3: Ablation of core components on Urban100 (

\times 4

). All variants use the same backbone and training steps (

T{=}120

Figure 3: Effect of LR-consistency across training steps.

	$T$ sweep				$\omega$ sweep				$d$ sweep
$T$	30	80	100	120	120	120	120	120	120	120	120	120
$\omega$	0.3	0.3	0.3	0.3	0.3	0.5	1.0	2.0	0.3	0.3	0.3	0.3
$d$	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.5	0.8	1.0	1.5
PSNR $\uparrow$	28.05	28.42	28.49	28.53	28.53	28.32	28.38	28.12	28.50	28.53	28.47	28.22
SSIM $\uparrow$	0.8440	0.8485	0.8494	0.8502	0.8502	0.8491	0.8488	0.8450	0.8495	0.8502	0.8427	0.8416
LPIPS $\downarrow$	0.1759	0.1697	0.1663	0.1647	0.1647	0.1654	0.1710	0.1769	0.1685	0.1647	0.1732	0.1761

Table 5: Sensitivity to training steps and hyperparameters on Urban100 (

\times 4

Figure 4: Qualitative ablation on Urban100 ( $\times 4$ ). LR, univariate, HR, and BATDiff results are shown.

Figure 5: Qualitative ablation on Set14 ( $\times 4$ ). LR, univariate, HR, and BATDiff results.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Parameter	Value
Optimizer	Adam
Initial learning rate	$1\times 10^{-3}$
Batch size	16
Training iterations	120k
Diffusion timesteps	100
Number of à trous levels	6

Appendix

Table 6: Implementation details used in all experiments.

Scales	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
4	27.92	0.8421	0.1712
5	28.21	0.8465	0.1680
6	28.53	0.8502	0.1647
7	28.49	0.8496	0.1651

Appendix

Table 7: Effect of the number of à trous levels on Urban100 (

\times 4

$\eta$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
0.1	28.12	0.8467	0.1689
0.3	28.53	0.8502	0.1647
0.5	28.28	0.8489	0.1668

Appendix

Table 8: Effect of LR-consistency step size on Urban100 (

\times 4

Model	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
Separate network per scale	28.41	0.8485	0.1669
Shared network (ours)	28.53	0.8502	0.1647

Appendix

Table 9: Shared vs. scale-specific denoisers on Urban100 (

\times 4

Reverse steps	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
50	28.11	0.8459	0.1698
75	28.36	0.8487	0.1672
100	28.53	0.8502	0.1647

Appendix

Table 10: Effect of reverse diffusion steps on Urban100 (

\times 4

Figure 6: Qualitative comparison on Urban100 under the $\times 8$ super-resolution setting.

Figure 7: Representative failure cases under the $\times 8$ setting. From left to right: Zoomed LR, ours, and HR reference. When the LR input contains extremely limited high-frequency information, the proposed method may produce slightly over-smoothed reconstructions or incomplete recovery of very fine architectural details.

Dataset	MetaSR [ 13 ]	LIIF [ 7 ]	LTE [ 19 ]	CLIT [ 6 ]	CiaoSR [ 4 ]	HIIF [ 15 ]	Ours $\times 6$
Set5	28.74	28.93	28.93	28.95	29.10	29.17	29.86
Set14	26.51	26.64	26.71	26.83	26.79	26.86	28.54
Urban100	23.99	24.20	24.28	24.44	24.58	24.59	24.66

Appendix

Table 11: Quantitative comparison for

\times 6

super-resolution (PSNR).

Scale	Dataset	PSNR $\uparrow$
$\times 3.15$	Set5	33.26
	Set14	30.41
	Urban100	28.79
$\times 5.20$	Set5	30.35
	Set14	28.96
	Urban100	25.11

Appendix

Table 12: Performance of BATDiff for continuous super-resolution scales (PSNR).

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