BSN-Based Diffusion Branch in Denoising

• BSN-Based Diffusion Branch is a dual-branch framework that combines blind-spot network predictions with diffusion model denoising for effective self-supervised image restoration.
• It enhances denoising by providing structural priors that guide the reverse diffusion process, reducing artifacts and preserving local details.
• Empirical results on SIDD and DND benchmarks demonstrate superior PSNR and SSIM, confirming its advantage over previous self-supervised methods.

A BSN-Based Diffusion Branch refers to the integration of Blind-Spot Networks (BSNs) within diffusion-based generative frameworks, in particular for self-supervised real-world image denoising. The design leverages the BSN’s ability to generate semi-clean images without using paired ground truth, and uses these outputs to guide a diffusion-based denoising process. The central motivation is to overcome the limitations of both paradigms: BSNs can lose local detail due to spatial independence assumptions, while diffusion models lack effective structural priors in the absence of paired data. By merging the two, the resulting framework—exemplified by the Blind-Spot Guided Diffusion (BSGD) method—achieves state-of-the-art self-supervised denoising, outperforming previous techniques on challenging datasets such as SIDD and DND (Cheng et al., 19 Sep 2025).

1. Mathematical Formulation of the BSN-Based Diffusion Branch

The BSN-based branch is operationalized within a diffusion model as a time-dependent module. The standard blind-spot network is extended to take as input a noisy sample at any diffusion timestep $t$, denoted $x_t$, and to predict a semi-clean image $\hat{x}_{0|t}$:

$$\min_{\theta_b} \sum_t \Big\| f_b(x_t, x_0, t) - x_0 \Big\|_1$$

where:

• $x_0$ is the (unobserved) clean image,
• $x_t$ is a sample at forward diffusion time $t$,
• $f_b(\cdot)$ is the BSN-based, time-dependent denoising function parameterized by $\theta_b$.

In the reverse process, the BSN-based branch provides an explicit prior that is used to guide the sampling of the conventional diffusion branch. Considering the reverse Markov process of a standard diffusion model,

$$p_{\theta}(x_{t-1}|x_t) = \mathcal{N}\left(x_{t-1}; \mu_{\theta}(x_t, t), \sigma_t^2 \mathbf{I} \right),$$

the guided reverse process in BSGD is modeled as:

$$p_{u,b}(x_t|x_{t+1}, y) = Z \cdot p_u(x_t|x_{t+1}) \cdot p_b(y|x_t),$$

where $p_u(\cdot)$ is the unconditional (UNet) diffusion probability, $p_b(\cdot)$ is the guidance from the semi-clean BSN-based output, and $Z$ is a normalization constant.

The noise estimate at each reverse step is then a convex combination of predictions from both the BSN-based and the unconditional diffusion branches:

$$\epsilon(x_t) = w \, \epsilon_{fb}(x_t, x_0) + (1 - w) \, \epsilon_{fu}(x_t)$$

where $w$ is a tunable scalar.

The denoised image $\hat{x}_{t-1}$ at each step is updated as:

$$x_{t-1} = \sqrt{1-\alpha_{t-1}-\sigma_t^2}\,\epsilon(x_t) + \sqrt{\alpha_{t-1}}\,\hat{x}_{0|t} + \sigma_{t}\mathbf{z}$$

with $\alpha_t$ set by the noise schedule and $\mathbf{z}$ standard Gaussian noise.

2. Role within the Dual-Branch Diffusion Framework

In the BSGD architecture, the BSN-based diffusion branch acts as a structure prior. Its core roles are:

• Generating Semi-Clean Estimates: The BSN predicts image structure by learning from neighboring pixels without looking at the central noisy value, thus providing an estimate of clean content even in the absence of ground-truth pairs.
• Guiding the Diffusion Process: By supplying its output as a “soft prior” to the conventional UNet-based diffusion branch, the integration harnesses the strengths of both approaches—structural consistency from the BSN and fine detail/texture restoration from the diffusion branch.
• Enabling Self-Supervised Denoising: In scenarios without paired clean data, the BSN-based branch provides the necessary guidance to train and sample from the diffusion model without supervision.

Furthermore, BSGD incorporates a complementary replacement sampling step, in which certain pixels in the intermediate semi-clean outputs may be probabilistically replaced by their noisy counterparts from the input. This bolsters noise structure preservation and texture realism, particularly across weak or homogeneous regions.

3. Addressing Challenges in BSN and Diffusion Methods

BSNs, while effective for removing signal-dependent noise, often cause loss of fine local structure, introduce artifacts, and fail to exploit dependencies across different regions due to their inherent spatial independence assumptions. Conversely, vanilla diffusion models struggle to learn meaningful denoising mappings without paired data, leading to either mode collapse or visually implausible samples.

By fusing the BSN-based branch with a diffusion-based model, BSGD addresses these limitations:

• The semi-clean output from the BSN-based branch preserves coarse structure and object boundaries, providing an informative prior for the diffusion branch to recover local texture.
• During each diffusion step, the guidance from the BSN-based branch steers the sampling toward more plausible images, reducing artifacts such as patchiness and grid lines.
• The replacement sampling mechanism further enhances temporal consistency in the denoising cascade.

4. Empirical Evaluation and Quantitative Impact

Extensive experiments on SIDD and DND benchmarks demonstrate that BSGD, with its BSN-based diffusion branch, outperforms prior self-supervised denoising methods in both objective and perceptual metrics:

• SIDD: BSGD achieves a PSNR close to 38 dB, significantly exceeding previous self-supervised approaches.
• DND: BSGD similarly surpasses prior techniques.

Ablation studies confirm that both the inclusion of BSN-based guidance and the replacement sampling strategy are critical for performance. Removing the BSN branch or the replacement step leads to consistent drops in PSNR and SSIM, directly substantiating the necessity of the BSN-based diffusion branch.

5. Generalization and Broader Implications

The BSN-Based Diffusion Branch, as instantiated in BSGD, illustrates a general strategy for leveraging blind-spot predictions as “priors” in self-supervised generative modeling tasks beyond denoising. Similar architectural motifs—dual-branch frameworks wherein a structurally-informed branch guides or regularizes a data-driven generative branch—could plausibly be adapted for other inverse problems such as inpainting, deblurring, or data recovery in domains lacking paired ground truth.

6. Summary Table: BSN-Based Diffusion Branch in BSGD (Cheng et al., 19 Sep 2025)

Aspect	Technical Details	Empirical Findings
Branch design	Time-dependent BSN in diffusion framework	Guides UNet-based diffusion process
Guidance integration	Weighted combination of BSN and UNet noise estimates	Reduces grid artifacts, restores details
Replacement strategy	Pixel-wise mixing of BSN estimate and original noise	Enhances detail and texture preservation
Evaluation dataset	SIDD, DND	State-of-the-art PSNR, SSIM, visual quality
Supervision requirement	Self-supervised (no paired data)	Practical for real-world noisy datasets

In conclusion, the BSN-Based Diffusion Branch enables effective, artifact-free, and self-supervised denoising by synergistically merging blind-spot structural priors with diffusion-based generative modeling. This approach demonstrates empirical superiority on real-world benchmarks and offers a template for future dual-branch designs in unsupervised and self-supervised image restoration.