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Zero-Shot Low-Light Image Enhancement via HMC-Based Diffusion Posterior Refinement with Phase Constraints

This paper proposes a zero-shot low-light image enhancement framework that leverages a pretrained diffusion model as a prior and refines its predictions via Hamiltonian Monte Carlo sampling under Fourier phase constraints to effectively suppress noise, preserve structural details, and ensure measurement consistency without additional training.

Original authors: Jiahua Liu, Yang Zheng, Ji Li, Zhaoqiang Liu

Published 2026-09-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jiahua Liu, Yang Zheng, Ji Li, Zhaoqiang Liu

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Photography under the cover of darkness has always been a battle against the grain. When light is scarce, cameras struggle to capture a clear picture, often returning an image that is not just dark, but speckled with chaotic noise and washed-out colors. The goal of low-light image enhancement is to rescue these degraded scenes, turning a muddy, grainy mess into something bright, clear, and true to life. For years, scientists have tried to solve this by teaching computers to recognize what a normal photo looks like, using massive libraries of paired images—dark ones and their bright counterparts—to learn the transformation. However, this approach has a major flaw: it relies on having the perfect training data, which is often impossible to get for every unique lighting condition or camera type. When the real world presents a situation the computer hasn't seen before, these systems often fail, producing images that look fake, overly bright, or still full of noise.

A new approach, developed by researchers at the University of Electronic Science and Technology of China and Capital Normal University, sidesteps the need for this specific training data entirely. Instead of teaching a computer what a photo should look like through examples, they use a powerful, pre-existing tool known as a diffusion model. Think of this tool as a highly experienced artist who has seen millions of natural scenes and understands the fundamental rules of how light, shadow, and texture interact. This artist doesn't need to be taught how to fix a specific dark photo; they simply know what a realistic image looks like in general. The researchers' innovation lies in how they guide this artist. Rather than letting the artist guess and then correcting the guess with simple math, they use a sophisticated sampling technique called Hamiltonian Monte Carlo. This method allows the system to explore many possible versions of the restored image, moving through the possibilities with a kind of calculated momentum to find the one that is both realistic and perfectly matches the original dark photo's structure.

The core of this new method, which the team calls HMC-DiffPC, treats the restoration of a dark image as a puzzle where two pieces of information must be balanced. One piece is the "prior," or the general knowledge of what a natural image looks like, provided by the pre-trained diffusion model. The other piece is the "likelihood," which is the strict requirement that the final result must still look like the original dark photo, just brighter and cleaner. In many previous attempts, the system would try to fix the image by taking small, direct steps based on the difference between the guess and the original. This often led the system into a local trap, where it would get stuck in a solution that looked okay but missed the finer details or introduced new errors. The researchers replaced this direct stepping with a process that simulates physical motion. By introducing an imaginary momentum, the system can roll over small bumps in the landscape of possibilities, exploring a wider range of options before settling on the best answer. This ensures the final image is not just a guess, but a refined version that respects the original scene's layout.

To make sure the restored image didn't lose its sharp edges or structural integrity, the team added a specific rule based on the mathematics of waves. They realized that while the brightness of a photo can change, the underlying structure—the edges of buildings, the shape of clouds, the outline of a tree—is encoded in a specific part of the image's frequency data, known as the phase. The researchers decided to lock this phase information from the original dark photo and force the new, brighter image to keep it. This acts as a rigid skeleton, ensuring that even as the computer fills in the missing light and smooths out the noise, the fundamental shape of the scene remains exactly where it belongs. This prevents the common problem where enhanced images look smooth but blurry, or where details like clouds or distant trees dissolve into a soft haze.

The results of this approach were tested on a variety of real-world datasets, including images taken in extremely low light and those with no reference to what the scene originally looked like. The team found that their method consistently produced better results than other techniques that do not require training on specific data. In comparisons, the new method was able to suppress noise more effectively while keeping the image details sharp, outperforming previous zero-shot methods that often introduced visible artifacts or failed to brighten the image enough. When compared to methods that were trained on massive datasets, this new approach held its own, proving that it could generalize well to different types of lighting and noise without ever having seen them before. The researchers also noted that while the process involves complex calculations, it does not require the massive computational power usually associated with such tasks, making it a practical solution for real-world use.

Ultimately, this work demonstrates that the best way to fix a dark photo might not be to teach a computer to memorize every possible scenario, but to give it a deep, general understanding of what a picture is and then guide it with strict rules about what the specific scene must preserve. By combining the generative power of modern artificial intelligence with the physical laws of how images are structured, the researchers have created a tool that can see clearly in the dark without needing a map. The findings suggest that for tasks where data is scarce or the conditions are unpredictable, relying on these robust, pre-existing models and refining them with careful mathematical constraints offers a path forward that is both powerful and reliable. The method stands as a testament to the idea that sometimes, the most effective solution is not to learn more, but to explore the possibilities more deeply.

Technical Summary: Zero-Shot Low-Light Image Enhancement via HMC-Based Diffusion Posterior Refinement with Phase Constraints

Problem Statement
Low-light image enhancement (LLIE) aims to recover visually pleasing and structurally faithful images from degraded observations characterized by insufficient illumination and severe noise. While traditional methods (e.g., histogram equalization, Retinex-based decomposition) are computationally efficient, they often amplify noise and fail in extremely dark regions. Supervised deep learning approaches achieve strong performance on matched training distributions but suffer from poor generalization to unseen illumination or noise patterns due to distribution shifts. Furthermore, the collection of large-scale paired datasets is expensive and often impractical. Existing zero-shot and unsupervised methods alleviate the need for paired supervision but frequently struggle with severe noise and complex degradations, often producing hallucinated textures, residual noise, or overexposed regions when relying on simple gradient-based corrections.

Methodology
The authors propose HMC-DiffPC, a zero-shot framework that performs Hamiltonian Monte Carlo (HMC)-based diffusion posterior refinement under frequency-domain phase constraints. The method utilizes a pretrained diffusion model (DM) as an implicit natural image prior within a regularized data-fitting formulation, requiring no additional training.

The core methodology consists of three main components:

Diffusion Posterior Refinement via HMC:
Instead of enforcing measurement consistency through first-order gradient corrections (which can lead to local minima and biased trajectories), the authors formulate the refinement objective as a posterior inference problem. They define an energy function $U(\bar{x}_0; \hat{x}_0)$ combining a measurement likelihood term (based on a heteroscedastic Gaussian noise model approximating Poisson noise) and a quadratic regularization term centered on the diffusion model's prediction $\hat{x}_0$ .
To sample from the resulting posterior distribution, the method employs HMC. By introducing auxiliary momentum variables and simulating Hamiltonian dynamics, HMC enables the sampler to traverse the energy landscape more effectively than standard gradient descent, allowing for transitions across energy barriers and reducing the risk of getting stuck in local minima. This process refines the diffusion prediction by balancing the generative prior with measurement consistency.
Frequency-Domain Phase Constraints:
Recognizing that structural and geometric information is primarily encoded in the phase component of the Fourier domain, the authors introduce a phase constraint during the posterior refinement. Specifically, the phase component of the observed low-light image is preserved and combined with the amplitude component of the diffusion-generated estimate. This strategy enforces structural alignment with the original measurement, preserving edge fidelity and suppressing artifact amplification while allowing the diffusion model to restore illumination and details.
Algorithmic Workflow:
The process operates iteratively over diffusion timesteps. At each step, the diffusion model predicts a clean image estimate. This estimate undergoes phase constraint (replacing its phase with that of the input low-light image). Subsequently, HMC sampling is performed to refine this phase-constrained estimate by minimizing the defined energy function. The final output is reconstructed after the reverse diffusion process completes.

Key Contributions

HMC-Based Posterior Refinement: The paper introduces the use of Hamiltonian Monte Carlo to sample from a diffusion-induced posterior distribution for LLIE. This approach moves beyond simple gradient-based corrections, offering a more robust exploration of the solution space that better integrates generative priors with measurement likelihoods.
Phase Constraint Integration: The authors propose a novel mechanism to preserve structural integrity by enforcing frequency-domain phase constraints derived from the input low-light image during the refinement process. This ensures that the enhanced image retains the geometric structure of the original observation.
Zero-Shot Framework: The method relies solely on a pretrained unconditional diffusion model (trained on ImageNet) and requires no task-specific retraining or paired data, addressing the limitations of data scarcity and distribution shifts.

Experimental Results
Extensive experiments were conducted on five benchmark datasets: LOLv1, LOLv2, and LSRW (paired), and LIME and DICM (unpaired/no-reference).

Quantitative Performance: HMC-DiffPC consistently outperformed existing zero-shot methods (e.g., GDP, Zero-IG, FourierDiff, LLIEDiff) and most unsupervised approaches. It achieved competitive performance against supervised methods, notably attaining the best results on the LSRW, LIME, and DICM datasets, demonstrating strong cross-dataset generalization.
Qualitative Improvements: Visual comparisons indicated that the proposed method produces more visually pleasing results with clearer structural details and sharper edges compared to baselines. It effectively suppressed noise while avoiding the overexposure and structural loss observed in other diffusion-based methods.
Ablation Studies:
- Optimization Strategy: HMC outperformed gradient descent, heavy-ball momentum, Langevin dynamics, MALA, and DAPS, confirming that the improvement stems from the specific sampling dynamics rather than just additional optimization steps.
- Phase Constraint: Removing the phase constraint resulted in lower performance, validating its role in preserving structural consistency. The performance gap between using the measurement phase and the ground-truth phase was small, suggesting the input phase is a reliable prior.
- Noise Modeling: The heteroscedastic Gaussian approximation used in the method proved superior to Anscombe and direct Poisson formulations for diffusion posterior refinement.

Significance and Claims
The paper claims that HMC-DiffPC provides a robust solution for zero-shot low-light image enhancement. By reframing the correction step as a posterior inference problem and utilizing HMC for sampling, the method achieves improved structural stability and reduces artifact amplification compared to conventional gradient-based diffusion approaches. The integration of phase constraints further ensures that the enhanced images maintain geometric consistency with the original observations. The authors assert that their approach offers a strong balance between leveraging powerful pretrained generative priors and adhering to physical measurement constraints, making it effective across diverse datasets without the need for retraining.

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