Digital photography image fusion aims to integrate essential information from multiple source images. However, the current methods predominantly rely on a single-channel fusion strategy, failing to fully leverage color pixel information. Furthermore, the significant variations in fusion mechanisms across tasks limit the performance of generic models. These factors can lead to color shifts and the loss of fine details. To address these issues, we propose a novel approach named MRQE-Net for general digital photography image fusion. The proposed network treats RGB pixels as a unified entity by encapsulating them into reduced biquaternion (RQ), and achieves task-specific fusion through mixture of RQ experts (MoRQE) module within a unified model. Specifically, we first develop the RQ spatial attention (RQSA) and RQ multi-scale pixel attention (RQMSPA) modules to enhance salient features. Then, we propose the deep feature invertible module (DFIM) to efficiently extract the complementary deep information. Finally, to enable customized fusion and feature enhancement for each task, we propose the adaptive feature synthesis amplification module (AFSAM). To the best of our knowledge, this is the first attempt to perform digital photography image fusion in RQ neural networks. Extensive experiments demonstrate that the MRQE-Net outperforms state-of-the-art methods across multiple metrics for each subtask.

Composition—the ability to generate myriad variations from finite means—is believed to underlie powerful generalization. However, compositional generalization remains a key challenge for deep learning. A widely held assumption is that learning disentangled (factorized) representations naturally supports this kind of extrapolation. Yet, empirical results are mixed, with many generative models failing to recognize and compose factors to generate out-of-distribution (OOD) samples. In this work, we investigate a controlled 2D Gaussian "bump" generation task with fully disentangled $(x,y)$ inputs, demonstrating that standard generative architectures still fail in OOD regions when training with partial data, by re-entangling latent representations in subsequent layers. By examining the model’s learned kernels and manifold geometry, we show that this failure reflects a "memorization" strategy for generation via data superposition rather than via composition of the true factorized features. We show that when models are forced—through architectural modifications with regularization or curated training data—to render the disentangled latents into the full-dimensional representational (pixel) space, they can be highly data-efficient and effective at composing in OOD regions. These findings underscore that disentangled latents in an abstract representation are insufficient and show that if models can represent disentangled factors directly in the output representational space, it can achieve robust compositional generalization.

Diffusion models are capable of generating photo-realistic images that combine elements which do not appear together in natural images, demonstrating their ability to compositionally generalize. Nonetheless, the precise mechanism of compositionality and how it is acquired through training remains elusive. Here, we consider a highly reduced setting to examine whether diffusion models learn semantically meaningful and fully factorized representations of composable features. We performed extensive controlled experiments on conditional DDPMs trained to generate various forms of 2D Gaussian data. We demonstrate that the models learn factorized, semi-continuous manifold representations that are orthogonal in underlying continuous latent features of independent variations but are not aligned for different values of the same feature. With such representations, models demonstrate superior compositionality but have limited ability to interpolate over unseen values of a given feature. Our experimental results further demonstrate that diffusion models can attain compositionality with a small amount of compositional examples, suggesting a novel way to train DDPMs. Finally, we connect manifold formation in diffusion models to percolation theory in physics, thereby offering insights into the sudden onset of factorized representation learning. Our thorough toy experiments thus contribute a deeper understanding of how diffusion models capture compositional structure in data, paving the way for future research aimed at enhancing factorization and compositional generalization in generative models for real-world applications.