1. Bibliographic Information

• Title: Stable Diffusion Segmentation for Biomedical Images with Single-step Reverse Process
• Authors: Tianyu Lin, Zhiguang Chen, Zhonghao Yan, Weijiang Yu, and Fudan Zheng.
• Affiliations: The authors are affiliated with Sun Yat-sen University and Beijing University of Posts and Telecommunications in China.
• Journal/Conference: This paper is a preprint available on arXiv. The link provided (https://arxiv.org/abs/2406.18361) points to an e-print repository widely used in fields like computer science for rapid dissemination of research before or during the formal peer-review process.
• Publication Year: 2024 (based on the arXiv submission date).
• Abstract: The paper addresses the challenges of applying diffusion models to medical image segmentation, namely their high computational cost, slow inference due to a multi-step reverse process, and the need for multiple samples to achieve stable predictions. To solve these issues, the authors propose SDSeg, the first latent diffusion model for segmentation based on Stable Diffusion. SDSeg introduces a "latent estimation" strategy to enable a single-step reverse process and a "latent fusion concatenation" method to eliminate the need for multiple samples. Experiments on five benchmark datasets show that SDSeg outperforms state-of-the-art methods while being significantly more efficient and stable, capable of producing reliable predictions with just one reverse step and one sample.
• Original Source Link:
  • arXiv Page: https://arxiv.org/abs/2406.18361
  • PDF Link: http://arxiv.org/pdf/2406.18361v3

2. Executive Summary

• Background & Motivation (Why):

  • Core Problem: Diffusion Probabilistic Models (DPMs), despite their generative power, are notoriously inefficient for medical image segmentation. Existing DPM-based methods operate in the high-dimensional pixel space, requiring massive computational resources and time. Furthermore, they rely on a slow, iterative "reverse process" (denoising) over many steps and often need to average the results from multiple random samples to produce a single, reliable segmentation map. This makes them impractical for clinical use where speed and consistency are critical.
  • Identified Gaps:
    1. Pixel-Space Inefficiency: Generating binary segmentation masks in pixel space is wasteful, as these masks contain far less complex information than natural images.
    2. Multi-Step Inference: The standard requirement of 10-1000 reverse steps makes inference extremely slow.
    3. Prediction Instability: The generative nature of diffusion models means that different runs with different initial noise produce slightly different results, a lack of consistency that is undesirable in medical applications.
  • Innovation: The paper introduces SDSeg, a model that tackles these problems by building on Stable Diffusion (SD), a type of Latent Diffusion Model (LDM). The key idea is to perform the diffusion process not on the images themselves, but in a much smaller, compressed "latent space." This immediately reduces computational cost. The authors then introduce specific architectural and training innovations to achieve single-step, single-sample, stable inference.

• Main Contributions / Findings (What):

  • First Latent Diffusion Model for Segmentation: SDSeg is presented as the first segmentation model built directly on the powerful and efficient Stable Diffusion framework.
  • Single-Step Reverse Process: A novel latent estimation loss is introduced. This loss directly supervises the model to predict the final, clean latent representation from a noisy one in a single shot, bypassing the need for a gradual, multi-step denoising process.
  • Single-Sample Stability: The paper replaces the standard cross-attention mechanism for conditioning with a simpler concatenate latent fusion. This direct fusion of image and mask information is more efficient and robust, eliminating the need to generate and average multiple predictions.
  • State-of-the-Art Performance & Efficiency: Extensive experiments show that SDSeg surpasses existing methods on five diverse biomedical datasets. Crucially, it achieves this with a fraction of the computational resources and an inference speed up to 100 times faster than previous diffusion-based segmentation models.

3. Prerequisite Knowledge & Related Work

• Foundational Concepts:

  • Biomedical Image Segmentation: This is the task of partitioning a medical image (like a CT scan or a colonoscopy image) into different segments or regions. For example, identifying and outlining a tumor, an organ, or a polyp. It is a critical step for diagnosis, treatment planning, and monitoring disease progression.
  • Diffusion Probabilistic Models (DPMs): These are a class of powerful generative models. They work in two stages:
    1. Forward Process: Gradually add random noise to a real image over a series of timesteps until it becomes pure, indistinguishable noise. This process is fixed and doesn't involve learning.
    2. Reverse Process: Train a neural network (typically a U-Net architecture) to reverse this process. Starting from random noise, the network learns to gradually remove the noise step-by-step to generate a realistic image. This reverse process is what makes DPMs slow, as it requires many sequential steps.
  • Latent Diffusion Models (LDMs) / Stable Diffusion (SD): Instead of adding noise to high-resolution images in pixel space, LDMs first compress the image into a much smaller, lower-dimensional "latent" representation using an autoencoder. The forward and reverse diffusion processes are then performed in this computationally cheaper latent space. Once the denoising is complete, a decoder part of the autoencoder converts the final latent representation back into a full-resolution image. Stable Diffusion is the most famous LDM.
  • U-Net: A convolutional neural network architecture specifically designed for biomedical image segmentation. Its "U" shape consists of a downsampling path (encoder) to capture context and an upsampling path (decoder) to enable precise localization, with "skip connections" that pass feature maps from the encoder to the decoder to preserve fine-grained details. The denoising network in most diffusion models uses a U-Net-like structure.

• Previous Works:

  • Traditional Segmentation Models (CNNs & ViTs): Models like U-Net, DeepLabV3+, and Vision Transformer (ViT)-based models like TransU-Net have been the standard for medical image segmentation. They are typically deterministic and fast but may lack the generative expressiveness of DPMs.
  • Image-Level Diffusion Segmentation: Prior works like MedSegDiff and Diff-U-Net applied the diffusion concept to segmentation. However, they performed the diffusion process directly on the pixel-level segmentation masks. The paper argues this is inefficient (unnecessary) and leads to the high computational costs and slow inference that SDSeg aims to solve. These models also required multiple reverse steps and averaging multiple samples to stabilize predictions.

• Differentiation:

  • SDSeg's primary innovation is moving the entire process into the latent space of a pre-trained Stable Diffusion model. This is a fundamental shift from previous diffusion segmentation models.
  • While standard LDMs still use a multi-step reverse process, SDSeg introduces a latent estimation loss that trains the model for single-step inference.
  • Instead of relying on the complex cross-attention mechanism for conditioning (guiding the generation with an input image), SDSeg uses a simple and effective concatenation of latent representations, which is better suited for image-to-image tasks and improves stability.

4. Methodology (Core Technology & Implementation)

SDSeg's architecture is elegantly built upon the Stable Diffusion framework, with three key modifications to adapt it for efficient and stable medical image segmentation.

该图像是示意图，展示了论文中SDSeg模型的整体架构。图中从像素空间到潜在空间的扩散过程与反向去噪过程，以及条件信息的拼接策略清晰呈现了模型训练和推理的流程。

As shown in Figure 1, the model operates in three spaces:

1. Pixel Space (Input/Output): This is where the original medical image C and the ground-truth segmentation map X exist. The final prediction is also generated here.
2. Conditioning (Input Image Processing): The medical image C is processed by a trainable vision encoder $\tau_{\theta}$ to produce a conditioning latent representation $z_c$.
3. Latent Space (Diffusion Process): The core diffusion process happens here. A pre-trained autoencoder's encoder $\mathcal{E}$ converts the segmentation map X into its latent representation $z_0$. The denoising U-Net operates on noisy versions of $z_0$ conditioned by $z_c$.

• Principles & Steps:

  1. Encoding:

     • The input medical image $C \in \mathbb{R}^{H \times W \times 3}$ is passed through the trainable vision encoder to get its latent representation: $z_c = \tau_{\theta}(C)$.
     • The ground truth segmentation map $X \in \mathbb{R}^{H \times W \times 3}$ is passed through the frozen encoder of a pre-trained autoencoder to get its latent representation: $z = \mathcal{E}(X)$. This is the "clean" latent at timestep 0, denoted as $z_0$. The autoencoder is from the original Stable Diffusion model and is kept frozen, as it is already effective at compressing binary masks (see Figure 2).

  2. Forward Diffusion (Training):

     • A random timestep $t$ is sampled.
     • Gaussian noise $n$ is added to the clean latent $z_0$ to create a noisy latent $z_t$, following the standard DPM formula: $$z _ { t } = \sqrt { \bar { \alpha } _ { t } } z _ { 0 } + \sqrt { 1 - \bar { \alpha } _ { t } } n$$
       • Symbol Explanation:
         • $z_t$: The noisy latent representation at timestep $t$.
         • $z_0$: The original, clean latent representation of the segmentation map.
         • $n$: Random Gaussian noise.
         • $\bar{\alpha}_t$: A hyperparameter from a predefined noise schedule that controls the amount of noise added at step $t$. As $t$ increases, $\bar{\alpha}_t$ decreases, meaning more noise is added.

  3. Denoising & Loss Calculation (Training):

     • The denoising U-Net $f(\cdot)$ takes the noisy latent $z_t$ and the conditioning latent $z_c$ (fused via concatenation) as input and predicts the noise that was added: $\tilde{n} = f(z_t, z_c)$.
     • The standard noise prediction loss is calculated: $\mathcal{L}_{noise} = \mathcal{L}(\tilde{n}, n)$.

4.1 Latent Estimation

This is the core innovation for enabling single-step inference. The authors reason that for simple segmentation maps, a powerful denoising network should be able to predict the final clean latent directly, without needing many refinement steps.

• Procedure: After the network predicts the noise $\tilde{n}$, they algebraically rearrange the forward process equation to directly estimate the clean latent $\tilde{z}_0$: $$\tilde { z } _ { 0 } = \frac { 1 } { \sqrt { \bar { \alpha } _ { t } } } ( z _ { t } - \sqrt { 1 - \bar { \alpha } _ { t } } \tilde { n } )$$
  • Symbol Explanation:
    • $\tilde{z}_0$: The estimated clean latent representation.
    • All other symbols are as defined previously.
• Latent Estimation Loss: A new loss term is introduced to directly supervise this prediction. It measures the difference between the estimated clean latent $\tilde{z}_0$ and the true clean latent $z_0$: $\mathcal{L}_{latent} = \mathcal{L}(\tilde{z}_0, z_0)$
• Final Loss Function: The total loss is a weighted sum of the noise prediction loss and the latent estimation loss: $$\mathcal { L } = \mathcal { L } _ { n o i s e } + \lambda \mathcal { L } _ { l a t e n t }$$
  • Symbol Explanation:

    • $\lambda$: A weight to balance the two loss terms. The paper sets $\lambda=1$.

    • The loss function $\mathcal{L}$ used for both terms is the mean absolute error (L1 loss).

      By training the model to minimize $\mathcal{L}_{latent}$, the denoising U-Net is explicitly optimized to predict the final clean latent in a single step, making the multi-step reverse process unnecessary during inference.

4.2 Concatenate Latent Fusion

Standard Stable Diffusion uses a cross-attention mechanism to inject conditioning information (e.g., a text prompt) into the denoising U-Net. The authors argue this is overly complex and inefficient for image-to-image tasks like segmentation.

• Motivation: As shown in Figure 2, the latent representation of a segmentation map retains strong spatial correlation with the original map. This suggests that spatial feature fusion methods from classic segmentation networks (like U-Net) would be effective.

• Procedure: Instead of cross-attention, SDSeg simply concatenates the conditioning latent $z_c$ with the noisy latent $z_t$ along the channel dimension before feeding them into the denoising U-Net. This is a simpler, faster, and more direct way to provide the model with the spatial information from the input image needed to guide the segmentation. This also contributes to prediction stability, removing the need for multiple samples.

  该图像是图表，展示了BTCV、STS、REF和CVC四个医学图像数据集上的输入原图、标签、重建图像及其4倍放大的潜在表示，表达了潜在空间编码$z=\mathcal{E}(X)$和对应解码重构$\widetilde{X}=\mathcal{D}(z)$的关系。

4.3 Trainable Vision Encoder

To effectively extract features from diverse medical images, the vision encoder $\tau_{\theta}$ is made trainable.

• Architecture & Initialization: The vision encoder $\tau_{\theta}$ has the same architecture as the autoencoder's encoder $\mathcal{E}$. It is initialized with the same pre-trained weights from Stable Diffusion (which were trained on natural images).
• Fine-tuning: Unlike the autoencoder, which remains frozen, the vision encoder is fine-tuned during training. This allows it to adapt from extracting features for natural images to extracting features relevant for specific medical segmentation tasks (e.g., focusing on polyps or organs), enhancing its versatility and performance across different imaging modalities. Figure 6 in the Appendix visually demonstrates this adaptation process.

5. Experimental Setup

• Datasets: Experiments were conducted on five public benchmark datasets covering different imaging modalities and segmentation tasks.

  This is a manual transcription of the data in Table 1.

  Task	Dataset	Target	Training Data	Test Data
  2D Binary Segmentation	CVC-ClinicDB (CVC)	Polyp	488 images	62 images
  	Kvasir-SEG (KSEG)	Polyp	800 images	100 images
  	REFUGE2 (REF)	Optic Cup	800 images	400 images
  3D Binary Segmentation	BTCV	Abdomen Organ	18 volumes	12 volumes
  	STS-3D (STS)