Global-Local Latent Consistency Model

Updated 4 July 2026

The paper introduces a dual-path diffusion framework that decouples global bone suppression from local texture preservation in CXR imaging.
It leverages lung segmentation, latent consistency objectives, and Poisson blending to effectively remove ribs and clavicles while retaining fine details.
Empirical evaluations show superior PSNR/LPIPS improvements and a roughly 10% computational cost compared to standard diffusion-based methods.

Searching arXiv for the cited GL-LCM paper and closely related background papers on latent consistency models, diffusion backbones, and CXR bone suppression.
Global-Local Latent Consistency Model (GL-LCM) is a bone suppression architecture for chest X-ray (CXR) imaging that was introduced to achieve fast high-resolution suppression of ribs and clavicles while preserving pulmonary texture detail [2508.03357]. In this formulation, the method combines lung segmentation, dual-path diffusion sampling in latent space, and global-local fusion in pixel space. Its central premise is that bone suppression in CXR requires the simultaneous handling of two distinct objectives—global suppression of low-frequency bone structures and preservation of high-frequency local textures—and that processing both objectives through a single end-to-end network often leads to detail blurring or incomplete suppression [2508.03357].

1. Clinical problem and modeling rationale

CXR-based pulmonary diagnosis is complicated by the presence of bone structures that can obscure diagnostically relevant image content. Recent deep learning work, particularly diffusion-based modeling, has been identified as promising for minimizing the visibility of bones in CXR images, but the reported limitations of existing diffusion-based methods are twofold: difficulty in balancing complete bone suppression against local texture preservation, and high computational demand with extended processing time [2508.03357].

GL-LCM addresses these limitations by decoupling the suppression problem into a global path and a local path. The global path targets ribs and clavicles as low-frequency structures, whereas the local path focuses on retaining fine pulmonary textures. The outputs of these two samplers are then fused in pixel space so that the final reconstruction inherits strong suppression from the global path and fine-detail retention from the local path [2508.03357].

This design places GL-LCM within a broader class of models that separate shared/global structure from local or complementary detail. However, in the CXR setting the distinction is operational rather than merely representational: the decomposition is used to mitigate clinically relevant failure modes such as boundary artifacts and detail blurring during bone suppression [2508.03357].

2. Latent-space formulation and consistency objective

The model is defined over a high-resolution pixel space and a compressed latent space. The pixel domain is
$X \subseteq \mathbb{R}^{H\times W}$ for CXR images, with $H=W=1024$, while the latent space is
$Z \subseteq \mathbb{R}^{h\times w\times c}$, with $(h,w,c)\ll(H,W,3)$, obtained through a VQGAN encoder $E:X\to Z$ and decoder $D:Z\to X$ [2508.03357]. This encoder-decoder choice links the method to the VQGAN line of latent image modeling [2012.09841].

Two conditional latents are defined. The global latent $\widetilde z_g$ is the embedding of the full CXR image $I$. The local latent $\widetilde z_l$ is the embedding of the lung-masked image $M(I)\odot I$, where $M(I)\in{0,1}^{H\times W}$ is a lung mask produced by a pre-trained Dense-U-Net [2508.03357]. The distinction between $\widetilde z_g$ and $\widetilde z_l$ is the formal basis for the model’s global-local consistency mechanism.

GL-LCM adopts the Latent Consistency Model framework [2310.04378]. Let $z_0\in Z$ be a clean latent and $t\in{1,\dots,T}$. The forward noising process is

$$
z_t=\sqrt{\bar\alpha_t}\,z_0+\sqrt{1-\bar\alpha_t}\,\epsilon,\qquad \epsilon\sim\mathcal{N}(0,I),
$$

where $\bar\alpha_t=\prod_{s=1}^t\alpha_s$ and $\alpha_s=1-\beta_s$ [2508.03357]. The training objective is the LCM noise-prediction loss

$$
\mathcal{L}(\theta)=\sum_{t=1}^{T\mathbb{E}{z_0,\epsilon}\bigl|\epsilon\theta(z_t,t,\widetilde} z)-\epsilon\bigr|_2^2.
$$

The reverse denoising step is implemented with schedules involving $c_{\mathrm{skip}}$, $c_{\mathrm{out}}$, and $\sigma_t$ [2508.03357]. The noise estimator backbone is a U-Net with multi-resolution attention, following the diffusion backbone family associated with Dhariwal and Nichol [2105.05233].

A key implication of this setup is that consistency is enforced in latent space rather than by direct pixel-level multitask optimization. This suggests that GL-LCM treats the suppression-preservation tradeoff as a conditional generation problem with structured conditioning, rather than as a purely deterministic image-to-image regression problem.

3. Architectural composition

The architecture has three principal stages: lung segmentation, dual-path diffusion sampling in latent space, and global-local fusion via Poisson blending [2508.03357].

Component	Input or condition	Function
Lung segmentation	$I$	Computes $M(I)$ using a pre-trained Dense-U-Net
Global path	$\widetilde z_g = E(I)$	Standard conditional LCM sampling for $T=50$ steps, producing $z_g$
Local path	$\widetilde z_l = E(M(I)\odot I)$	LCM sampling with Local-Enhanced Guidance, producing $z_l$
Fusion	$S_g=D(z_g)$, $S_l=D(z_l)$	Poisson blending to obtain final result $R$

The global path uses the full-image latent condition $\widetilde z_g=E(I)$ and performs standard conditional LCM sampling for $T=50$ steps to produce a global latent $z_g$ [2508.03357]. This path is responsible for strong suppression of globally organized bone structure.

The local path uses the lung-masked condition $\widetilde z_l=E(M(I)\odot I)$ and introduces Local-Enhanced Guidance (LEG) to mitigate boundary artifacts and blurred details associated with naive local conditioning. LEG modifies the score estimate through a weighted combination of gradients:

\nabla_{z_{l,t}}\log p\bigl(z_{l,t}\mid\widetilde z_l,\widetilde z_g\bigr)

\alpha_l\,\nabla_{z_{l,t}}\log p\bigl(z_{l,t}\mid\widetilde z_l\bigr)
+
(1-\alpha_l)\,\nabla_{z_{l,t}}\log p\bigl(z_{l,t}\mid\widetilde z_g\bigr),
$$

with $\alpha_l=3$ in the reported experiments [2508.03357]. An important property of LEG is that it addresses these issues without additional training.

After sampling, both latent outputs are decoded into pixel space:

$$
S_g=D(z_g),\qquad S_l=D(z_l).
$$

The final image $R$ is then obtained by solving a Poisson blending problem:

$$
\begin{cases}
\nabla\cdot(\nabla R)=\nabla\cdot(\nabla S_l), & \text{in } M(I),\
R=S_g, & \text{outside } M(I).
\end{cases}
$$

This fusion mechanism preserves local high-frequency gradients within the lung mask while inheriting global low-frequency content elsewhere [2508.03357]. In operational terms, the fusion stage is what converts two independently sampled latent reconstructions into a single radiographic output with region-specific frequency behavior.

4. Training regime and inference pipeline

Training is split between the latent autoencoding module and the diffusion-style noise estimator. The VQGAN encoder-decoder is trained for 300 epochs with batch size 4, Adam, and initial learning rate $1\times10^{-4}$. The noise estimator $\epsilon_\theta$ is trained for 600 epochs with batch size 4, AdamW, and initial learning rate $1\times10^{-4}$ [2508.03357]. The noise schedule uses $\beta_t$ linearly from $0.00085$ to $0.012$ over $T=50$ steps. The losses include the LCM noise-prediction term and standard VQGAN reconstruction, adversarial, and perceptual losses [2508.03357].

Inference follows a fixed six-step procedure [2508.03357]:

Compute the lung mask $M(I)$.
Encode $\widetilde z_g=E(I)$ and $\widetilde z_l=E(M(I)\odot I)$.
Perform global-path sampling for 50 steps to obtain $z_g$.
Perform local-path sampling for 50 steps with LEG to obtain $z_l$.
Decode $S_g=D(z_g)$ and $S_l=D(z_l)$.
Apply Poisson fusion to produce the final result $R$.

For $1024\times1024$ images, inference on an A100 GPU takes on average 8.54 s, reported as approximately 10% of standard diffusion-based methods [2508.03357]. This timing is central to the model’s intended role in settings where high spatial resolution and practical throughput are both required.

5. Empirical evaluation

GL-LCM is evaluated on a self-collected dataset, SZCH-X-Rays, and the public JSRT dataset [2508.03357]. SZCH-X-Rays contains 741 paired CXR/DES soft tissue images with train/validation/test splits of 592/74/75. JSRT contains 241 pairs with train/validation/test splits of 192/24/25. All images are resized to $1024\times1024$, and negatives are applied for JSRT [2508.03357].

The reported evaluation metrics are Bone Suppression Ratio (BSR, %), MSE $(\times 10^{{-3})\downarrow$,} PSNR $(\mathrm{dB})\uparrow$, and LPIPS $\downarrow$ [2508.03357]. Quantitative results are organized into Table 1 for SZCH-X-Rays, Table 2 for JSRT, and Table 3 for inference efficiency. The paper states that the model delivers superior bone suppression and remarkable computational efficiency, significantly outperforming several competitive methods [2508.03357].

The ablation studies clarify the contribution of individual components. For local guidance, Table 4 compares vanilla local conditioning, CFG, and LEG. LEG improves PSNR by $+0.57$ dB on SZCH and $+0.34$ dB on JSRT, while LPIPS improves by $-3.45\%$ and $-25.7\%$, respectively; Figure 4 is reported to show boundary artifacts corrected by LEG [2508.03357]. For fusion strategy, Table 5 compares no fusion (global only), $\alpha$-blend, AE-based fusion, and Poisson Fusion. Poisson Fusion yields the best PSNR/LPIPS gains, including a $+1.99$ dB PSNR gain on SZCH [2508.03357].

These ablations are significant because they isolate two separate error sources: conditioning-induced local artifacts and post-decoding fusion quality. The reported gains indicate that the model’s performance is not attributable solely to latent diffusion in general, but to the combination of LEG and Poisson-based global-local recombination.

6. Limitations, reproducibility, and terminology

The reported limitations are specific and implementation-relevant. Segmentation errors in the lung mask $M(I)$ can degrade local context and lead to slight artifacts. In addition, the dual-path design doubles latent sampling cost, although the method remains fast because $T=50$ [2508.03357]. These limitations follow directly from the architecture: the local path depends on segmentation quality, and the decoupled design incurs duplicated sampling effort.

The implementation is intended to be reproducible. Code and trained models are available at the project repository, and the implementation notes specify PyTorch 2.0.1 together with training and inference scripts. The README is described as containing instructions for data preparation, environment setup, and hyperparameter configuration [2508.03357].

The acronym “GL-LCM” is not universal across arXiv literature and should be disambiguated carefully. In the CXR paper, it denotes “Global-Local Latent Consistency Models” for bone suppression [2508.03357]. By contrast, the robotics paper “Global Prior Meets Local Consistency: Dual-Memory Augmented Vision-Language-Action Model for Efficient Robotic Manipulation” uses “LCM” to mean “Local Consistency Memory” inside the OptimusVLA framework rather than a latent consistency model [2602.20200]. Likewise, CoCoNet’s formulation around global consistency and local complementarity addresses multi-view self-supervised representation learning rather than bone suppression or latent diffusion-based CXR generation [2209.07811]. A common misconception is therefore to treat “global-local consistency” as naming a single standardized architecture; the literature instead uses related terminology for different mechanisms in different domains.

Within medical image generation, GL-LCM is most precisely understood as a latent-space diffusion system specialized for high-resolution CXR bone suppression, with decoupled global and local conditional sampling and Poisson-domain recombination as its defining traits [2508.03357].