Diffusion-Based Denoising
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Training-free object removal commonly redirects self-attention away from the target region, but on few-step distilled diffusion models this often leaves object-shaped residuals. We identify a temporal mismatch: a structured prediction forms inside the mask at the first forward, and the short trajectory offers few later chances to revise it, while attention rerouting acts mainly in later steps. Across four distilled backbones, magnitude-matched single-forward interventions show that background-directed state correction affects the final result more than attention rerouting. We therefore propose ReState, which corrects the masked clean prediction toward background evidence retrieved from the input using a noise-level-aware weight that vanishes at the final forward. ReState retains object-excluding attention as a complementary constraint and adds no denoiser evaluations. Across two paired benchmarks and two few-step backbones, ReState achieves the best masked PSNR, SSIM, and LPIPS among training-free methods, improving PSNR by 3.17 dB on average over the strongest baseline. On OBER-Test, it also outperforms the 50-step attention-forcing reference on all three metrics at 6.7x lower latency. The same configuration transfers to two additional distilled backbones without retuning. Project page: https://tdrlee.github.io/ReState
AReA: Adaptive Receptive-Field Attention for Efficient High-Resolution Diffusion Transformers
Generating images beyond the training resolution of Diffusion Transformers (DiTs) remains challenging, as the number of tokens grows rapidly with resolution, full attention becomes expensive, and outputs often suffer from structural distortions and degraded detail. We identify uniform full attention as the common source of both problems. Attending to all tokens at every step causes quadratic cost and exposes the model to more tokens and relative distances beyond the training range, pushing the model out of distribution. We observe that attention's effective receptive field narrows during denoising, from global in early steps that form structure to local in later steps that refine details. We propose AReA, a training-free attention mechanism whose receptive field evolves from coarse to fine, following the denoising progression. In early steps, AReA applies cross-scale coarse attention over downsampled keys and values, capturing global context, while in later steps it applies local attention within progressively shrinking windows. Without additional parameters or training, experiments show that AReA consistently outperforms state-of-the-art training-free baselines across target resolutions and different models, while also being faster and more efficient.
APEX: Asynchronous Prefix Denoising for Extreme Compression
Fewer latent tokens promise cheaper diffusion. Yet aggressive latent compression creates a reconstruction-generation dilemma: adding channels improves reconstruction but makes generation harder. We introduce APEX, short for Asynchronous Prefix denoising for EXtreme compression, which pairs a hierarchical latent space with asynchronous denoising over channel groups. Our autoencoder orders channel prefixes from structure to detail, while one shared denoiser generates them at staggered local times without adding tokens. On ImageNet-512, APEX outperforms existing methods at every evaluated channel count under 64x and 128x compression. At matched training and guided sampling compute, it also outperforms a 256-token model at every evaluated budget, with larger gains at lower compute. Code is available at https://daviddinkevich.github.io/APEX.
PreviewDiff: Multimodal Critic-Guided Search over Diffusion Latents
Diffusion models can produce striking images and videos, but they still struggle with the compositional details that make a generation faithful to a prompt, such as object counts, attribute binding, spatial relations, and temporally grounded actions. A common way to improve prompt satisfaction is to spend more compute at test time through Best-of-N sampling, but final-sample selection is fixed. Best-of-N can only choose among completed outputs and cannot repair a promising trajectory before it fails. We introduce PreviewDiff, a training-free test-time search method that turns diffusion sampling from scalar search into a multimodal critic-guided search over intermediate latents. At selected denoising checkpoints, PreviewDiff decodes a partial preview, asks a multimodal judge to score and critique it, and uses the resulting natural-language feedback to branch over semantic prompt edits and locally re-noised latent continuations. These branches are then scored and selectively rolled forward, allowing verifier compute to guide generation while the sample is still editable. Across image and video generation benchmarks, PreviewDiff consistently improves over budget-matched Best-of-N selection and strong scalar-search baselines. Ablations show that earlier interventions and increased search width provide the largest gains, while deeper search and additional semantic variants offer complementary improvements. PreviewDiff demonstrates that multimodal feedback is most useful not only as a final verifier, but as an active controller inside the denoising process.
Unlocking Few-Step Diffusion for Faithful Previews
Sampling latency compounds in diffusion workflows, where users generate and discard many candidates before keeping one. Surprisingly, the poor outputs of standard few-step samplers do not reflect a lack of reconstruction capacity: by optimizing only the initial noise, frozen 3-4-step samplers can closely reproduce their corresponding full-step outputs. Building on this finding, we learn corrections to the initial noise and denoising updates using endpoint supervision, improving correspondence with full-step outputs generated from the same noise and prompt. The resulting previews allow users to screen candidates cheaply and reserve full-step generation for promising ones. Input correction also transfers across sampling budgets without retraining. Experiments show substantial improvements in reference fidelity, including 53-78% lower reconstruction MSE than retrained LD3 on unconditional benchmarks, alongside improved ranking preservation and candidate selection on SD1.5, SDXL, and FLUX.1-dev.
Fill2SR: Repurposing Inpainting Diffusion Transformers for Real-World Super-Resolution
Recent real-world image super-resolution (SR) methods often adapt text-to-image (T2I) backbones with ControlNet-style branches or spatial conditioning tokens, which increases memory and computes with resolution and often constrains training to a fixed scale. We propose Fill2SR, which repurposes a masked-inpainting Diffusion Transformer for SR without extra spatial branches. Our Inpainting-Interface Evidence Adapter (IIEA) writes the low-quality (LQ) observation into the native masked-image slot under a full-image mask, turning inpainting into a reverse-degradation conditional rectified flow trained with LoRA-only tuning. We further introduce RCDT, an offline pipeline that distills degradation descriptors from unpaired real images and transfers them onto clean targets using frozen open-source models. Fill2SR supports mixed-resolution training up to QHD and yields stable performance across outputs. On synthetic benchmarks, our base model with IIEA achieves the best LPIPS on DIV2K and LSDIR; adding RCDT trades a small LPIPS drop for consistently stronger no-reference quality on RealLQ250 and RealPhoto60. Fill2SR remains memory-predictable, running inference on a single 32GB GPU and extending to multi-megapixel outputs via tiled restoration.
PixelDiT2: Representation-Grounded Pixel Diffusion Transformers
Recent advances in pixel-space diffusion models have narrowed the image quality gap with latent-space diffusion, but still converge more slowly and lag behind in final image quality. We argue that a key reason is the lack of an explicit representation prior: unlike latent diffusion, which usually denoises in a compact and structured latent space, pixel diffusion needs to learn denoising-friendly representations and pixel generation simultaneously from raw RGB space. To address this problem, we propose PixelDiT2, an end-to-end pixel-space diffusion model designed to decouple representation learning from pixel generation without introducing an autoencoder or latent reconstruction bottleneck. We propose representation grounding that uses a frozen pretrained vision foundation model to provide explicit per-patch representation guidance throughout denoising, allowing the pixel diffusion transformer to focus more on pixel generation. On ImageNet-256x256, PixelDiT2 achieves an FID of 1.46 after 600 epochs; at 512x512 resolution, PixelDiT2 achieves an FID of 1.48 after 680 epochs. Project page: https://pixeldit.github.io/pixeldit2/
Denoising Diffusion Generative Models Secretly Calculate Attentions
Denoising diffusion models are the dominant architecture for image generation, whereas most natural language generation and modeling are primarily handled by well-known transformer architectures employing attention mechanism. Here, we show that diffusion models also inherently use an attention mechanism very similar to that of transformers. Therefore, attention emerges as a universal machine learning principle, based on a general training objective. We also show similarities in basic functional principle of auto-encoders and attention-based models. These equivalences allows us to interchange these designs based on practical requirements. As an example, we can reformulate the diffusion framework to reduce the lengthy training process and computation-intensive image generation. Using this approach, a simplified algorithm is proposed for image generation which is based on attention mechanism. Results show that the attention-based implementation achieves comparable performance with significantly less effort and computational resources.
Optimize Your Sampling: Tuned Diffusion Sampling with Bayesian Optimization
Sampling from a diffusion model typically requires many forward passes through a large neural network, making generation computationally expensive. While much work has focused on efficient solvers and samplers, comparatively little attention has been paid to selecting the sampling timesteps themselves. A recent line of work optimizes theoretically derived surrogates for sample quality rather than the quality metric itself. We propose Optimizing Your Sampling (OYS), which instead treats timestep selection as a black-box optimization problem, optimizing the target metric directly with Bayesian optimization. OYS outperforms both the default schedules and those of Align Your Steps on text-to-image generation, and improves over the default schedules on inpainting and other image tasks, in both quantitative and human evaluations. OYS requires no additional training, is applicable even to distilled models, and improves both simple and sophisticated samplers such as Euler and DPM-Solver++. A 5-step OYS schedule retains 89%-94% of the quality of a 50-step schedule while reducing inference cost by 10x.
DualStabSleepNet: A Dual-Domain Diffusion Stabilization Network for Robust Sleep Staging
Existing deep learning approaches for automatic sleep staging suffer from limited robustness under heterogeneous recording conditions, where non-stationary noise, inter-subject differences and cross-dataset distribution shifts cause unstable features and poor generalization. This work proposes DualStabSleepNet (DSSNet), a dual-domain diffusion stabilization network for robust sleep staging, which improves robustness in both data and feature domains. After preprocessing multi-channel polysomnography (PSG), a continuous-scale diffusion-based stabilization module suppresses noise while preserving physiological signal structures. Stabilized signals are converted to time-frequency representations and fed into a Vision Transformer backbone. A teacher-student guided diffusion feature stabilization module further mitigates feature drift and enforces multi-level feature consistency. Evaluated on four public PSG datasets SleepEDF-20, SleepEDF-78, SHHS and ISRUC-S3, DSSNet achieves state-of-the-art accuracy of 89.2%, 88.0%, 89.7%, 86.7% with improved macro-F1 and Cohen's kappa. It obtains notable improvements on hard transitional stages (e.g., 12.5% gain for N1 on SHHS) and boosts N2/REM recognition. Under cross-dataset settings, DSSNet is robust to distribution shift and performs on par with or superior to target-dataset trained baselines, demonstrating its practical potential for real-world sleep staging across heterogeneous cohorts.
StyleComposer: Training-Free Multi-Reference Style Composition
The style of a painting is not monolithic: color, texture, and structure may come from different sources. Existing reference-guided methods transfer them as one style signal, leaving each attribute's source and strength outside the user's control. We ask where in a diffusion model one attribute can change while the others hold, and find that no single representation isolates all three. The proposed StyleComposer therefore routes each style attribute through the representation where it separates best and coordinates the routes over denoising time. Without training or inversion, it satisfies three references and the prompt jointly more closely than prior methods, and exposes one strength slider per attribute. Project page: https://lexxsh.github.io/StyleComposer
Rectify Then Diffuse: Disentangling Concepts Before Denoising Trajectory Unfolds
Text-to-image diffusion models can generate individual concepts well, but they often omit or merge concepts incorrectly with multiple concepts. We trace these failures to an early coordination bottleneck: before denoising begins, prompt-conditioned attention may allocate different concepts to strongly overlapping spatial support, which can keep their attention coupled as denoising proceeds. This observation motivates treating compositional generation as a boundary-condition problem rather than repeatedly controlling the evolving trajectory. To this end, we propose Rectify-then-Diffuse (RTD), a training-free framework that rectifies the initial allocation once before standard denoising. Firstly, we propose Soft-Overlap Disentanglement (SOD), which converts normalized overlap between pilot concept maps into a differentiable and layout-agnostic separation objective. Secondly, we introduce Isotropic Gradient Rectification (IGR), which normalizes the SOD gradient and applies a bounded latent displacement with a consistent scale across prompts and initializations. Extensive experiments show that RTD achieves state-of-the-art compositional fidelity and robust gains. On the AE-Bench object pair subset, RTD improves BLIP-VQA by 45.8% and ImageReward by 19.6% over CO3 while running 2.3 faster. Code will be released at https://github.com/Z-yiwei/rectify-then-diffuse
FeatFix: Reuse What You Verify through Local Exact-Feature Correction for Faster Cached Diffusion Inference
Diffusion models are widely used to generate high-quality images and videos, but their iterative denoising process remains computationally intensive. A growing class of training-free accelerators reduces this cost by reusing cached intermediate features or forecasting future ones. To control draft drift, these methods sometimes compute an exact block feature for verification. Yet the resulting exact feature is typically used only to measure discrepancy or guide a later decision and is then discarded. We find that this previously computed feature can instead be reused for correction. Forwarding it at the verification site resets the local draft residual and reduces downstream feature error. Based on this observation, we introduce FeatFix, a local exact-feature correction method for cached diffusion inference. FeatFix operates at a fixed sparse set of layer--timestep sites. At each selected site, it replaces the complete draft block output with the exact output computed from the same incoming state, avoiding token- or channel-level partial replacement and full-timestep recomputation. Experiments across four image and video backbones show that FeatFix consistently accelerates generation, achieving a speedup of up to over Vanilla while maintaining competitive output quality.
FARI: Robust One-Step Inversion for Watermarking in Diffusion Models
Inversion-based watermarking is a promising approach to authenticate diffusion-generated images, yet practical use is bottlenecked by inversion that is both slow and error-prone. While the primary challenge in the watermarking setting is robustness against external distortions, existing approaches over-optimize internal truncation error, and because that error scales with the sampler step size, they are inherently confined to high-NFE (number of function evaluations) regimes that cannot meet the dual demands of speed and robustness. In this work, we have two key observations: (i) the inversion trajectory has markedly lower curvature than the forward generation path does, making it highly compressible and amenable to low-NFE approximation; and (ii) in inversion for watermark verification, the trade-off between speed and truncation error is less critical, since external distortions dominate the error. A faster inverter provides a dual benefit: it is not only more efficient, but it also enables end-to-end adversarial training to directly target robustness, a task that is computationally prohibitive for the original, lengthy inversion trajectories. Building on this, we propose FARI (Fast Asymmetric Robust Inversion), a one-step inversion framework paired with lightweight adversarial LoRA fine-tuning of the denoiser for watermark extraction. While consolidation slightly increases internal error, FARI delivers large gains in both speed and robustness: with approximately 20 minutes of fine-tuning on a single NVIDIA RTX A6000 GPU, it surpasses 50-step DDIM inversion on watermark-verification robustness while dramatically reducing inference time. Code and pretrained models are available at https://github.com/0xD009/FARI.
Noise-Free One-Step LoRA for Task-Driven Image Restoration with Diffusion Priors
Degraded images not only reduce visual quality but also impair downstream high-level vision tasks. Task-driven image restoration (TDIR) addresses this issue by jointly optimizing restoration quality and task performance. Recent works show that pretrained diffusion priors benefit TDIR, yet diffusion-based restoration is inherently stochastic, as the sampling process depends on a random noise term, which can undermine task consistency. In this paper, we show that a deterministic, noise-free one-step forward pass with pretrained diffusion priors can substantially improve TDIR, but the benefit critically depends on the adaptation module: LoRA yields consistent gains, whereas ControlNet-style conditioning does not. This enables one-step forwarding that surpasses conventional multi-step diffusion TDIR baselines. Furthermore, we introduce a task-preserving GAN training strategy that improves perceptual quality without sacrificing task performance. Extensive experiments on classification, segmentation, and detection demonstrate consistent gains over prior TDIR methods, and we further validate generalization on real-world degraded images and OCR.
ScaleResfusion: Residual Rectified Flow based on Residual Vector Field
Real-world Image Restoration (Real-IR) aims to recover high-quality (HQ) images from complex and unknown degradations. Recent diffusion-based methods have substantially improved perceptual quality, yet two obstacles remain: methods that sample from Gaussian noise require many steps and are often less faithful to the degraded input, whereas residual-based methods that start from the low-quality (LQ) image typically train task-specific models from scratch, with optimization objectives coupled to a particular noise scheduler, and therefore cannot reuse modern pre-trained generative priors. We present ScaleResfusion, which rewrites residual restoration as a scheduler-independent adaptation interface for pre-trained text-to-image rectified-flow models. Its core, Residual Rectified Flow (RRF), inserts the residual term into the linear transport path of Rectified Flow, so that sampling starts from noisy LQ at an exact acceleration point, where the signal-to-noise ratio of the starting state is continuously controlled by the residual ratio . The resulting optimization target, the residual vector field, contains no scheduler-specific coefficients and differs from the pre-trained rectified-flow target only by the residual offset ; adapting a frozen billion-scale backbone therefore reduces to fitting this compact residual correction with LoRA-only training. A knowledge-distillation pipeline built around RRF further reduces sampling to as few as 4 steps. Experiments on real-world super-resolution across multiple benchmarks show that ScaleResfusion achieves state-of-the-art restoration quality and transfers consistently across pre-trained rectified-flow backbones from 2B to 9B parameters.
Nuclear Quantum Effects as a Denoising Problem
Nuclear quantum effects are rigorously captured by imaginary-time path integrals, which map the quantum Boltzmann distribution onto a ring polymer of classical replicas. Yet the nuclear masses, the coupling to the environment, and the boundary conditions of the path remain hard-wired in the simulation or the trained model, even though this quantum context enters the path measure only through a quadratic action known in closed form. Here we show that a denoiser trained on classical Boltzmann statistics alone, composed at sampling time with an analytic Gaussian component carrying the entire quantum context, yields the quantum Boltzmann distribution of the nuclei. Such a composition exists and is exact whenever the training noise does not exceed the intrinsic quantum uncertainty of the target ensemble, and it is invariant across all quantum contexts admitted by this bound. We show exact transfer across temperature, isotopic mass, dissipation strength, and the boundary conditions of the path in theory and in numerical experiments, without retraining. The last yields the end-to-end displacement and momentum distributions of a tagged nucleus from open imaginary-time paths. The same invariance extends in principle to the permuted boundary conditions of bosonic exchange, with the identical denoiser. In this view, the noise of generative modeling and the quantum fluctuations of the nuclei are two faces of the same quadratic structure.
When to Plan, When to Polish: Noise Level as a Granularity Axis for Diffusion Language Models
Standard tokenwise diffusion LMs keep training corruption and inference commitment at token granularity throughout denoising. At high noise, this leaves scattered local fragments rather than coherent evidence, making it hard to form early coarse structure, exactly what planning-sensitive generation requires. Hierarchical planning methods add coarse stages to separate planning from wording, but they need extra planners, block latents, or two stage designs. We propose Noise Dependent Granularity Control (NDGC), a single-level diffusion method that uses the noise level as a granularity cue. NDGC aligns training exposure and inference commitment with denoising progress. High noise steps use coherent token groups to support early meaning commitment, while low noise steps return to token level refinement. This creates planning like coarse to fine denoising without an explicit planner or hierarchical architecture. Across controlled tests, ablations, and WritingPrompts, NDGC shows earlier skeleton formation, better ordered recovery, and healthier outputs.
Show the Signal, Hide the Noise: Spectral Forcing for Pixel-Space Diffusion
Pixel-space diffusion models are trained on full-bandwidth noisy images, yet the useful signal available to the denoiser is strongly frequency dependent. Under rectified-flow diffusion and natural-image power-law spectra, the per-band data-to-noise contour separates a signal-bearing low-frequency region from a noise-dominated high-frequency region at each time . We show that this implicit coarse-to-fine structure is not merely descriptive: it induces a capacity-allocation problem. A standard pixel-space denoiser must discover the moving bandwidth boundary internally and can spend computation on frequency-time regions where the optimal prediction collapses to deterministic baselines rather than data-distribution modeling. To make this boundary explicit, we introduce Spectral Forcing, a parameter-free, time-conditional 2D-DCT low-pass operator applied to the noisy input before the patch embedder. Its cutoff expands monotonically with the diffusion time and becomes the identity at the data endpoint. Through controlled synthetic experiments, we identify the regime in which the operator is beneficial: coarse patch tokenization and data whose high-frequency content is predominantly noise rather than essential signal. On ImageNet-256 with JiT-700M/32, Spectral Forcing consistently improves both FID and Inception Score across different training epochs, demonstrating robust gains throughout training; at finer tokenization, the spectral forcing is still competitive. We further insert the unchanged operator into SenseNova-U1, a unified text-to-image model, where it improves DPG-Bench and GenEval, showing that the input-side spectral prior transfers beyond class-conditional generation. These results suggest a route to capacity-efficient pixel-space diffusion by showing the signal and hiding the noise.
DuET: Dual Expert Trajectories for Diffusion Image Editing
Recent diffusion editors perform diverse instruction-based edits while conditioning on the source image at every denoising step. Yet persistent source-image conditioning can limit how fully an edit is executed and how natural the result appears, especially when the target scene diverges substantially from the input. We introduce DuET (Dual Expert Trajectories), a training-free inference method that temporarily relaxes source-image conditioning by transitioning through a text-to-image phase before returning to edit mode, allowing the denoising trajectory to move toward the target distribution while retaining the structural benefits of image-conditioned editing. Without modifying model weights or increasing sampling cost, DuET consistently improves instruction relevance, semantic fidelity, and perceptual quality across diverse models and benchmarks. In some cases, these gains come with a modest reduction in source-image preservation, revealing a predictable trade-off between source preservation and edit fidelity.
AsyncPatch Diffusion: spatially-flexible image generation
Standard diffusion models corrupt an entire sample with a single shared noise level, forcing all spatial regions to follow the same denoising trajectory. We introduce AsyncPatch Diffusion, a joint-diffusion framework that assigns distinct noise levels to different input dimensions, such as image pixels, or latent tokens. We show how this asynchronous corruption defines a valid generative process while supporting a richer family of spatially heterogeneous denoising trajectories, and prove the first valid ELBO for this process. We show that a single pretrained model can perform spatially adaptive generation, where different regions are denoised on different schedules. A key challenge is training: naive independent noise-level sampling overemphasizes highly heterogeneous configurations and underrepresents homogeneous noise levels, that are crucial during sampling. We address this with a controlled noise-level sampler that regulates both the average corruption level and its spatial variability. AsyncPatch achieves generation quality comparable to conventional diffusion on ImageNet 256 and LSUN, while being natively suited for inpainting without task-specific fine-tuning. We further introduce input guidance, which uses clean or partially corrupted regions to guide the generation of unknown regions, improving local consistency and texture matching. Finally, we demonstrate adaptive generation strategies including uncertainty-guided acceleration and autoregressive sampling.
Efficient and Training-Free Single-Image Diffusion Models
We consider the problem of generating images whose internal structure -- defined by the distribution of patches across multiple scales -- matches that of a single reference image. Recent approaches address this problem by training a diffusion model on a single image. But even in this setting, training is computationally expensive and requires hours of optimization. Instead, we model the image using a dataset of its patches at different scales. As this dataset is finite and the dimensionality of its patches is small, the score function for a noisy patch can be computed tractably using an optimal, closed-form denoiser, eliminating the need for neural network training. We integrate this patch-based denoiser into an efficient, training-free image diffusion model, and we describe how our method connects to classical patch-based image restoration techniques. Our approach achieves state-of-the-art generation quality and diversity compared to trained single-image diffusion models, and we demonstrate applications, including unconditional image generation, text-guided stylization, image symmetrization, and retargeting. Further, we show that our approach is compatible with latent space diffusion, and we show multiple additional acceleration techniques to achieve megapixel single-image generation in one second, and gigapixel generation in minutes.
DEMON: Diffusion Engine for Musical Orchestrated Noise
We present DEMON, a real-time diffusion engine that makes the denoising process playable as a live musical instrument: a control surface both broad (many parameters shaped per-frame across the output) and responsive (each control taking effect as fast as its place in the denoising loop allows). Built on ACE-Step 1.5 and StreamDiffusion's ring-buffer architecture with TensorRT acceleration, it sustains up to 12.3 decoder completions per second for 60-second music on a single consumer GPU (RTX 5090), or 11.3 generations per second at our production ring-depth of 4. At these rates denoising parameters become viable as live performance controls, but the ring buffer propagates per-request changes only at its drain rate, a floor of S denoising steps. We contribute four mechanisms. (1) Per-slot heterogeneous denoise scheduling: each ring-buffer slot owns its timestep schedule, so a moving denoise slider is tracked without wiping the in-flight queue, where the upstream global-schedule design must rebuild and discard it. (2) Shared mutable per-step state, giving any parameter consulted at every solver step next-tick effect, bypassing ring-buffer drain. (3) Per-frame source blending: a sampling-time control on the standard SDE re-noise step, giving a framewise transformation-strength axis that complements scalar denoise scheduling. (4) Windowed VAE decode exploiting receptive-field analysis for an 8.0x decode speedup. Together these separate streaming-diffusion parameters into four propagation classes, by onset and convergence latency.
Filtered Posterior Mean Collections: A Unified Framework for Analytical Models of Diffusion Generalization
The neural-network denoising functions which form the backbone of image diffusion models are remarkably consistent in their generalization behaviour across a wide variety of network architectures and training procedure hyperparameters. A recent line of research has sought to model the outputs of these networks by aggregating posterior weighted averages of training dataset patches. In this work, we consolidate these approaches into a unified model class which we call Filtered Posterior Mean Collections (FPMCs). We define this model class using query precision vectors, response weights, and source distributions, and illustrate that existing methods are recoverable with specific choices of these design axes. Investigating each axis in turn, we find that FPMC performance can be improved with soft relaxations of prior patch-based methods, and through augmentations of source distributions. Applying these findings to an existing FPMC, we demonstrate consistent sample improvement across three natural image datasets.
Forward-Learned Discrete Diffusion: Learning how to noise to denoise faster
Discrete diffusion models are a powerful class of generative models with strong performance across many domains. For efficiency, however, discrete diffusion typically parameterizes the generative (reverse) process with factorized distributions, which makes it difficult for the model to learn the target process in a small number of steps and necessitates a long, computationally expensive sampling procedure. To reduce the gap between the target and model distributions and enable few-step generation, we propose Forward-Learned Discrete Diffusion (FLDD), which introduces discrete diffusion with a learnable forward (noising) process. Rather than fixing a Markovian forward chain, we adopt a non-Markovian formulation with learnable marginal and posterior distributions. This allows the generative process to remain factorized while matching the target defined by the noising process. We train all parameters end-to-end under the standard variational objective. Experiments on various benchmarks show that, for a given number of sampling steps, our approach produces a higher quality samples than conventional discrete diffusion models using the same reverse parameterization.
LENS: Low-Frequency Eigen Noise Shaping for Efficient Diffusion Sampling
Distilled diffusion models accelerate image generation by reducing the number of denoising steps, but often suffer from degraded image quality. To mitigate this trade-off, test-time optimization methods improve quality, yet their iterative nature incurs substantial computational overhead and leads to slow inference, limiting practical usability. Recent hypernetwork-based approaches amortize this process during training, but still require costly noise modulation in high-dimensional latent spaces. In this work, we propose LENS (Low-frequency Eigen Noise Shaping), an efficient noise modulation framework that operates in a low-dimensional subspace. Our approach is motivated by the observation that low-frequency components of the noise largely determine the global structure and visual fidelity of generated images. Based on this observation, we provide a theoretical justification for restricting modulation to the low-frequency subspace and derive a principled training objective. Building on this, LENS employs a lightweight, standalone network to selectively modulate these components, enabling efficient and targeted noise modulation. Extensive experiments demonstrate that LENS achieves competitive image quality while reducing FLOPs by 400-700, model parameters by 25-75, and inference-time overhead by 10-20 compared to prior methods.
SpecEdit: Training-Free Acceleration for Diffusion based Image Editing via Semantic Locking
Diffusion-based image editing offers strong semantic controllability, but remains computationally expensive due to iterative high-resolution denoising over all spatial tokens. Dynamic-resolution sampling reduces this cost by performing early steps at reduced resolution. However, existing approaches prioritize upsampling using low-level heuristics such as edge detection or channel variance, which are weakly aligned with editing semantics and may lead to structural inconsistency. Moreover, spatial regions are often upsampled without verifying whether semantic modification is actually required, resulting in redundant high-resolution computation and accumulated errors. Therefore, we propose SpecEdit, a training-free dynamic-resolution framework tailored for diffusion-based image editing. SpecEdit follows a draft-and-verify scheme: a low-resolution draft first estimates the semantic outcome, after which token-level discrepancies are used to identify edit-relevant tokens for high-resolution denoising, while the remaining tokens stay at a coarse resolution. Experiments on Qwen-Image-Edit and FLUX.1-Kontext-dev demonstrate up to 10x and 7x acceleration, while maintaining strong quality. SpecEdit is complementary to step distillation and other acceleration techniques, achieving up to 13x speedup when combined with existing methods. Our code is in supplementary material and will be released on GitHub.
Denoising, Fast and Slow: Difficulty-Aware Adaptive Sampling for Image Generation
Diffusion- and flow-based models usually allocate compute uniformly across space, updating all patches with the same timestep and number of function evaluations. While convenient, this ignores the heterogeneity of natural images: some regions are easy to denoise, whereas others benefit from more refinement or additional context. Motivated by this, we explore patch-level noise scales for image synthesis. We find that naively varying timesteps across image tokens performs poorly, as it exposes the model to overly informative training states that do not occur at inference. We therefore introduce a timestep sampler that explicitly controls the maximum patch-level information available during training, and show that moving from global to patch-level timesteps already improves image generation over standard baselines. By further augmenting the model with a lightweight per-patch difficulty head, we enable adaptive samplers that allocate compute dynamically where it is most needed. Combined with noise levels varying over both space and diffusion time, this yields Patch Forcing (PF), a framework that advances easier regions earlier so they can provide context for harder ones. PF achieves superior results on class-conditional ImageNet, remains orthogonal to representation alignment and guidance methods, and scales to text-to-image synthesis. Our results suggest that patch-level denoising schedules provide a promising foundation for adaptive image generation.
Transformers Learn the Optimal DDPM Denoiser for Multi-Token GMMs
Transformer-based diffusion models have demonstrated remarkable performance at generating high-quality samples. However, our theoretical understanding of the reasons for this success remains limited. For instance, existing models are typically trained by minimizing a denoising objective, which is equivalent to fitting the score function of the training data. However, we do not know why transformer-based models can match the score function for denoising, or why gradient-based methods converge to the optimal denoising model despite the non-convex loss landscape. To the best of our knowledge, this paper provides the first convergence analysis for training transformer-based diffusion models. More specifically, we consider the population Denoising Diffusion Probabilistic Model (DDPM) objective for denoising data that follow a multi-token Gaussian mixture distribution. We theoretically quantify the required number of tokens per data point and training iterations for the global convergence towards the Bayes optimal risk of the denoising objective, thereby achieving a desired score matching error. A deeper investigation reveals that the self-attention module of the trained transformer implements a mean denoising mechanism that enables the trained model to approximate the oracle Minimum Mean Squared Error (MMSE) estimator of the injected noise in the diffusion steps. Numerical experiments validate these findings.
Diffusion Denoiser Achievable Analysis for Finite Blocklength Unsourced Random Access
Polyanskiy proposed a framework for the unsourced multiple access channel (MAC) problem where users employ a common codebook in the finite blocklength regime. However, existing approaches handle channel noise before the joint decoder. In this work, we introduce a decoder compatible diffusion denoiser as a lightweight analysis within joint decoding. The score network is trained on samples drawn from the channel output distribution, making the method easy to integrate with existing code designs. In our theoretical analysis, we derive a diffusion-denoiser random-coding achievable bound that is strictly tighter. Simulations on existing decoders, including FASURA, MSUG-MRA and pilot-based method, show consistent performance gains with at least a improvement in required at a fixed error target.