Spatially Adaptive Noise Injection

Diffusion models achieve state-of-the-art image synthesis, with their generative trajectories fundamentally exhibiting a spectral bias, resolving low-frequency global structures early and high-frequency fine details later. Conventional stochastic differential equation (SDE) solvers fail to account for this dynamic, naively injecting uniform white noise throughout the entire process and misusing the finite energy budget. In this work, we establish a mathematical framework that reconsiders SDE inference as a targeted, frequency-decoupled energy transfer. Leveraging this framework, we introduce Colored Noise Sampling (CNS), a novel, training-free stochastic solver. Rather than injecting uniform white noise, CNS utilizes a dynamic, timestep- and frequency-dependent schedule that more efficiently allocates injected energy toward structurally unresolved frequency bands. By actively exploiting the model's inherent spectral bias, CNS systematically steers the generated distribution toward the true data manifold. Extensive experiments demonstrate that CNS significantly outperforms standard ODE and SDE baselines as a strictly plug-and-play, inference-time sampler substitution across diverse architectures (SiT, JiT, FLUX). Compared to standard sampling on ImageNet-256, CNS achieves substantial unguided FID reductions, improving from 8.26 to 6.27 on SiT-XL/2, 32.39 to 26.69 on JiT-B/16, and 11.88 to 8.31 on JiT-H/16, while yielding consistent relative FID improvements with Classifier-Free Guidance. Project page is available at https://hadardavidson.github.io/CNS/.

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.

Diffusion models have achieved remarkable success in synthesizing complex static and temporal visuals, a breakthrough largely driven by Classifier-Free Guidance (CFG). However, despite its pivotal role in aligning generated content with textual prompts, standard CFG relies on a globally uniform scalar. This homogeneous amplification traps models in a well-documented "detail-artifact dilemma": low guidance scales fail to inject intricate semantics, while high scales inevitably cause structural degradation, color over-saturation, and temporal inconsistencies in videos. In this paper, we expose the physical root of this flaw through the lens of differential geometry. By analyzing Tweedie's Formula, we reveal that CFG intrinsically performs a tangential linear extrapolation. Because the natural data manifold is highly curved, this uniform linear step introduces a severe orthogonal deviation. To keep the generation trajectory safely bounded, we formulate a theoretical upper bound for spatial and adaptive guidance. Based on these geometric insights, we propose Spatial Adaptive Multi Guidance (SAMG), a training-free and virtually zero-cost sampling algorithm. SAMG dynamically computes point-wise conditional guidance energy, applying a conservative minimum scale to high-energy boundary regions to preserve delicate micro-textures, while deploying an aggressive maximum scale in low-energy regions to maximize semantic injection. Extensive experiments across diverse image (SD 1.5, SDXL, SD3.5 Medium) and video (CogVideoX, ModelScope) architectures demonstrate that SAMG effectively resolves the detail-artifact dilemma, achieving superior semantic alignment, structural integrity, and temporal smoothness without any computational overhead.