This work introduces quantum-inspired tensor-network circuits as trainable transforms for image inpainting. Among the proposed architectures, the diagonal quantum Fourier transform (QFT) relaxation is invertible with O(N2logN) computational cost for N×N images, inherently preserving minimum coherence throughout training via its circuit structure and eliminating the need for explicit coherence penalties. Unconstrained gradient-based phase optimization (Riemannian-optimization free) enables efficient learning from randomly sampled training data, allowing the learned transform to generalize to test images observed through fixed sampling masks. Numerical tests show that the learned models outperform fixed transforms and per-image optimization while matching the performance of much larger unitary architectures, yet with far fewer parameters.
Quantum machine learning offers a compelling representational perspective: angle-encoded states inhabit Hilbert spaces in which periodic similarities and interactions can be expressed naturally. Realizing this perspective for visual recognition remains difficult, however, because present quantum neural networks are constrained by limited qubit counts, costly circuit simulation and measurement, noise, and unstable optimization on noisy intermediate-scale quantum devices. We investigate whether useful structural ideas from quantum models can instead be realized as scalable classical Transformer operations. We introduce QiT, a Quantum-inspired Transformer for vision tasks with three components: (i) angle-inspired encoding that maps image tokens to learned trigonometric Hilbert-space features analogous to quantum rotation-based state encoding; (ii) self-attention over these periodic features, inducing a classical cosine kernel approximated to quantum fidelity kernels; and (iii) gated multiplicative emulation, a trainable classical surrogate for interaction terms found in variational circuits. All components are differentiable tensor operations, so QiT claims neither quantum computation nor quantum speedup and retains the O(N2D) attention complexity of a standard Vision Transformer. Across image-classification benchmarks, QiT is competitive with a matched classical Transformer while avoiding the severe runtime cost observed for a small simulated quantum Transformer. QiT-B reaches 78.3% ImageNet-1K top-1 accuracy with 45.7M parameters and 11.5 GFLOPs. These results position QiT as a scalable baseline for isolating and evaluating quantum-motivated inductive biases in visual recognition.
We propose a novel training-free method for inpainting with off-the-shelf text-to-image models. While guidance-based methods in theory allow generic models to be used for inverse problems such as inpainting -- in practice their effectiveness is limited, leading to the necessity of specialized inpainting-specific models. In this work, we argue the missing ingredient for training-free generic model usage is proper optimization of the initial noise sample. We optimize the initial noise to approximately reproduce the unmasked image, in as few as tens of optimization steps, then use it with a conventional training-free inpainting method. Critically, we propose two core ideas that make this possible: (i) we perform linear approximation that avoids the costly and often impractical unrolling required to relate the initial noise sample to model output -- which potentially is why this relationship was previously overlooked; and (ii) perform spectral preconditioning by optimizing the initial noise sample in the spectral domain with Adam, which stabilizes the optimization. We demonstrate our method on various inpainting tasks, outperforming the state of the art. Project website: https://ubc-vision.github.io/sonic/
While 10B-level industrial foundation models have pushed the boundaries of image inpainting, their prohibitive computational costs severely hinder practical deployment. Constructing a highly optimized task-specific specialist offers a promising solution; however, extreme structural compression inevitably triggers a severe representation bottleneck. To conquer this, we propose Moebius, a highly efficient lightweight inpainting framework. We systematically reconstruct the diffusion backbone by introducing the Local-λ Mix Interaction (LλMI) block. Comprising Local-λ and Interactive-λ modules, it elegantly summarizes spatial contexts and global semantic priors into fixed-size linear matrices, preserving complex latent interactions while drastically shedding parameters. Furthermore, to unlock the full representational capacity of this highly compact architecture, we synergistically pair it with an adaptive multi-granularity distillation strategy. Operating strictly within the latent space to avoid expensive pixel-space decoding, this strategy dynamically balances multiple gradient-based losses to achieve high-fidelity alignment. Extensive experiments across natural and portrait benchmarks demonstrate that this optimal synergy enables Moebius to rival or even surpass the generation quality of the 10B-level industrial generalist FLUX.1-Fill-Dev. Remarkably, Moebius achieves this using less than 2% of the parameters (0.22B vs. 11.9B) while delivering a >15× acceleration in total inference time, setting a new efficiency standard for high-fidelity inpainting. Project page at https://hustvl.github.io/Moebius.