Diffusion-Based Denoising

This work presents a robust multi-class classification framework for handwritten digits that combines diffusion-driven feature denoising with a hybrid feature representation. Inspired by our previous work on brain tumor classification, the proposed approach operates in a feature space to improve the robustness to noise and adversarial attacks. This manuscript is submitted as an extended abstract rather than a full-length press-ready paper. First, the input images are converted into tight, interpretable exemplification using Non-negative Matrix Factorization (NNMF). In parallel, special deep features are extracted using a computational neural network (CNN). These integral features are combined into a united hybrid representation. The main objective of this work is to extend our previously validated two-class framework to a multi-class handwritten digit classification scenario. To improve robustness, a step diffusion operation is used in the feature space by gradually adding Gaussian noise. A feature denoiser network is trained to reverse this operation and rebuild clean representations from tilted inputs. The courteous features are then applied for multi-class classification. The suggested method is evaluated in both baseline and adversarial settings using AutoAttack. The experimental outcome present that the diffusion-based hybrid model is both effective and robust, the CNN baseline models outperforming while maintain powerful classification performance. These results explain the activity of feature-level diffusion defense for reliable multi-class handwritten digit classification.

Composed Image Retrieval (CIR) uses a reference image and a modification text as a query to retrieve a target image satisfying the requirement of modifying the reference image according to the text instructions''. However, existing CIR methods face two limitations: (1) frequency bias leading to Rare Sample Neglect'', and (2) susceptibility of similarity scores to interference from hard negative samples and noise. To address these limitations, we confront two key challenges: asymmetric rare semantic localization and robust similarity estimation under hard negative samples. To solve these challenges, we propose the Modification frEquentation-rarity baLance neTwork MELT. MELT assigns increased attention to rare modification semantics in multimodal contexts while applying diffusion-based denoising to hard negative samples with high similarity scores, enhancing multimodal fusion and matching. Extensive experiments on two CIR benchmarks validate the superior performance of MELT. Codes are available at https://github.com/luckylittlezhi/MELT.

Diffusion models have achieved remarkable success in generating high-fidelity content but suffer from slow, iterative sampling, resulting in high latency that limits their use in interactive applications. We introduce DRiffusion, a parallel sampling framework that parallelizes diffusion inference through a draft-and-refine process. DRiffusion employs skip transitions to generate multiple draft states for future timesteps and computes their corresponding noises in parallel, which are then used in the standard denoising process to produce refined results. Theoretically, our method achieves an acceleration rate of $\tfrac{1}{n}$ or $\tfrac{2}{n+1}$, depending on whether the conservative or aggressive mode is used, where $n$ denotes the number of devices. Empirically, DRiffusion attains 1.4$\times$-3.7$\times$ speedup across multiple diffusion models while incur minimal degradation in generation quality: on MS-COCO dataset, both FID and CLIP remain largely on par with those of the original model, while PickScore and HPSv2.1 show only minor average drops of 0.17 and 0.43, respectively. These results verify that DRiffusion delivers substantial acceleration and preserves perceptual quality.

Denoising diffusion models are widely used for high-quality image and video generation. Their performance depends on noise schedules, which define the distribution of noise levels applied during training and the sequence of noise levels traversed during sampling. Noise schedules are typically handcrafted and require manual tuning across different resolutions. In this work, we propose a principled way to design per-instance noise schedules for pixel diffusion, based on the image's spectral properties. By deriving theoretical bounds on the efficacy of minimum and maximum noise levels, we design ``tight'' noise schedules that eliminate redundant steps. During inference, we propose to conditionally sample such noise schedules. Experiments show that our noise schedules improve generative quality of single-stage pixel diffusion models, particularly in the low-step regime.

Guided diffusion sampling relies on approximating often intractable likelihood scores, which introduces significant noise into the sampling dynamics. We propose using adaptive moment estimation to stabilize these noisy likelihood scores during sampling. Despite its simplicity, our approach achieves state-of-the-art results on image restoration and class-conditional generation tasks, outperforming more complicated methods, which are often computationally more expensive. We provide empirical analysis of our method on both synthetic and real data, demonstrating that mitigating gradient noise through adaptive moments offers an effective way to improve alignment.

What is a diffusion model actually doing when it turns noise into a photograph? We show that the deterministic DDIM reverse chain operates as a Partitioned Iterated Function System (PIFS) and that this framework serves as a unified design language for denoising diffusion model schedules, architectures, and training objectives. From the PIFS structure we derive three computable geometric quantities: a per-step contraction threshold $L^*_t$, a diagonal expansion function $f_t(λ)$ and a global expansion threshold $λ^{**}$. These quantities require no model evaluation and fully characterize the denoising dynamics. They structurally explain the two-regime behavior of diffusion models: global context assembly at high noise via diffuse cross-patch attention and fine-detail synthesis at low noise via patch-by-patch suppression release in strict variance order. Self-attention emerges as the natural primitive for PIFS contraction. The Kaplan-Yorke dimension of the PIFS attractor is determined analytically through a discrete Moran equation on the Lyapunov spectrum. Through the study of the fractal geometry of the PIFS, we derive three optimal design criteria and show that four prominent empirical design choices (the cosine schedule offset, resolution-dependent logSNR shift, Min-SNR loss weighting, and Align Your Steps sampling) each arise as approximate solutions to our explicit geometric optimization problems tuning theory into practice.

Controllable diffusion generation often relies on various heuristics that are seemingly disconnected without a unified understanding. We bridge this gap with Diffusion Controller (DiffCon), a unified control-theoretic view that casts reverse diffusion sampling as state-only stochastic control within (generalized) linearly-solvable Markov Decision Processes (LS-MDPs). Under this framework, control acts by reweighting the pretrained reverse-time transition kernels, balancing terminal objectives against an $f$-divergence cost. From the resulting optimality conditions, we derive practical reinforcement learning methods for diffusion fine-tuning: (i) f-divergence-regularized policy-gradient updates, including a PPO-style rule, and (ii) a regularizer-determined reward-weighted regression objective with a minimizer-preservation guarantee under the Kullback-Leibler (KL) divergence. The LS-MDP framework further implies a principled model form: the optimal score decomposes into a fixed pretrained baseline plus a lightweight control correction, motivating a side-network parameterization conditioned on exposed intermediate denoising outputs, enabling effective gray-box adaptation with a frozen backbone. Experiments on Stable Diffusion v1.4 across supervised and reward-driven finetuning show consistent gains in preference-alignment win rates and improved quality-efficiency trade-offs versus gray-box baselines and even the parameter-efficient white-box adapter LoRA.

Cooperative perception lets agents share information to expand coverage and improve scene understanding. However, in real-world scenarios, diverse and unpredictable corruptions undermine its robustness and generalization. To address these challenges, we introduce CoopDiff, a diffusion-based cooperative perception framework that mitigates corruptions via a denoising mechanism. CoopDiff adopts a teacher-student paradigm: the Quality-Aware Teacher performs voxel-level early fusion with Quality of Interest weighting and semantic guidance, then produces clean supervision features via a diffusion denoiser. The Dual-Branch Diffusion Student first separates ego and cooperative streams in encoding to reconstruct the teacher's clean targets. And then, an Ego-Guided Cross-Attention mechanism facilitates balanced decoding under degradation by adaptively integrating ego and cooperative features. We evaluate CoopDiff on two constructed multi-degradation benchmarks, OPV2Vn and DAIR-V2Xn, each incorporating six corruption types, including environmental and sensor-level distortions. Benefiting from the inherent denoising properties of diffusion, CoopDiff consistently outperforms prior methods across all degradation types and lowers the relative corruption error. Furthermore, it offers a tunable balance between precision and inference efficiency.

Steering diffusion models toward conditions unseen during training typically requires either retraining with conditional inputs or per-step gradient computations, both of which incur substantial computational overhead. We present Noise-Aligned RFM Steering (NA-RFM), a general recipe for efficiently steering diffusion models without gradient guidance during inference, enabling fast controllable generation. The method combines two offline-computed signals: noise alignment, a high-noise correction from PCA statistics of the target examples and the full data, and Recursive Feature Machine (RFM) activation steering, which learns a target-discriminative direction from labeled forward-process activations. During sampling, noise alignment provides coarse control at high noise, while the RFM direction is reused over intermediate/late timesteps through lightweight activation edits. Experiments on CIFAR-10, ImageNet, CelebA, and fine-grained bird species show improved target accuracy over gradient-based post-hoc guidance baselines, improved FID on the class-guidance benchmarks, and substantial inference speedups. Code: https://github.com/isotrivial/na-rfm.

An accurate initial heading angle is essential for efficient and safe navigation across diverse domains. Unlike magnetometers, gyroscopes can provide accurate heading reference independent of the magnetic disturbances in a process known as gyrocompassing. Yet, accurate and timely gyrocompassing, using low-cost gyroscopes, remains a significant challenge in scenarios where external navigation aids are unavailable. Such challenges are commonly addressed in real-world applications such as autonomous vehicles, where size, weight, and power limitations restrict sensor quality, and noisy measurements severely degrade gyrocompassing performance. To cope with this challenge, we propose a novel diffusion denoiser-aided gyrocompass approach. It integrates a diffusion-based denoising framework with an enhanced learning-based heading estimation model. The diffusion denoiser processes raw inertial sensor signals before input to the deep learning model, resulting in accurate gyrocompassing. Experiments using both simulated and real sensor data demonstrate that our proposed approach improves gyrocompassing accuracy by 26% compared to model-based gyrocompassing and by 15% compared to other learning-driven approaches. This advancement holds particular significance for ensuring accurate and robust navigation in autonomous platforms that incorporate low-cost gyroscopes within their navigation systems.

Diffusion models generate conditional samples by progressively denoising Gaussian noise, yet the denoising trajectory can stall at visually plausible but low-quality outcomes with conditional misalignment or structural artifacts. We interpret this behavior as local optima in a surrogate quality landscape: Once early denoising commits to a suboptimal global structure, later steps mainly sharpen details and seldom correct the underlying mistake. While existing inference-time approaches explore alternative diffusion states via re-noising with fixed strength or direction, they exhibit limited capacity to escape steep quality plateaus. We propose Controlled Random Zigzag Sampling (Ctrl-Z Sampling),a scalable sampling strategy that detects plateaus in quality landscape via a surrogate score, and allocates exploration only when a plateau is detected. Upon detection, Ctrl-Z Sampling rolls back to noisier states, samples a set of alternative continuations, and updates the trajectory when a candidate improves the score, otherwise escalating the exploration depth to escape the current plateau. The proposed method is model-agnostic and broadly compatible with existing diffusion frameworks. Experiments show that Ctrl-Z Sampling consistently improves generation quality over other inference-time scaling samplers across different NFE budgets, offering a scalable compute-quality trade-off. Code available at: https://github.com/ShunqiM/Ctrl-Z-Sampling.