DOTS: Detail-Oriented Timestep Sampling

• Detail-Oriented Timestep Sampling (DOTS) is a method that biases timestep sampling using a Beta distribution to prioritize late, detail-critical denoising steps.
• DOTS improves fine-grained detail synthesis by allocating more focus on high-frequency textures, yielding superior FID_patch scores while retaining semantic integrity.
• The strategy integrates seamlessly with existing diffusion model architectures, reallocating learning focus without incurring additional computational overhead.

Detail-Oriented Timestep Sampling (DOTS) is a training and inference scheduling strategy for diffusion probabilistic models, designed to ensure that generative models devote proportionally greater representational capacity to timesteps crucial for fine-grained detail synthesis. DOTS originated in the context of ultra-high-resolution (UHR) text-to-image diffusion, where standard uniform or heuristic timestep sampling often under-trains the model on late, detail-critical denoising stages. The core premise is that image structure and detail emerge in different temporal segments of the denoising process; as such, the timestep sampling distribution should be explicitly biased to maximize high-frequency detail reconstruction.

1. Motivation and Conceptual Background

Ultra-high-resolution T2I diffusion models require synthesis of textures and visual details at scales where minor deficiencies are perceptible. Prior empirical and theoretical investigation ([Yi et al., NeurIPS 2024]; (Zhao et al., 23 Oct 2025)) has shown that:

• Early denoising steps predominantly recover low-frequency, global structure.
• Late denoising steps are primarily responsible for the generation of high-frequency, fine-grained details.

Conventional training and distillation schedules (e.g., uniform or logit-normal sampling, as in standard diffusion model pipelines) allocate sampling and learning effort evenly or in a balanced manner across all timesteps, irrespective of their relative importance for final image sharpness. This general approach leads to oversmoothing, weakened detail, and suboptimal FID_patch and local detail metrics in UHR settings.

DOTS asserts that explicitly skewing the training focus toward late-stage timesteps—where detailed textures and edges are formed—will improve high-frequency detail synthesis without detrimental effects on overall fidelity or semantic content.

2. Mathematical Formulation and Algorithmic Implementation

DOTS implements a non-uniform, right-skewed scheduling of denoising timesteps, realized through Beta-distribution-based sampling. At each iteration in the model update phase, the timestep $t$ is sampled as:

$t \sim \mathrm{Beta}(\alpha, \beta)$

with $\alpha < \beta$ (empirically, $\alpha=2$, $\beta=4$), biasing $t$ toward values near zero (late in the denoising trajectory, i.e., closer to the data manifold).

The probability density function is: $$\pi_{\mathrm{beta}}(t; \alpha, \beta) = \frac{1}{\mathrm{B}(\alpha, \beta)} t^{\alpha - 1} (1 - t)^{\beta - 1}$$ where $$\mathrm{B}(\alpha, \beta) = \frac{\Gamma(\alpha)\Gamma(\beta)}{\Gamma(\alpha + \beta)}$$ is the Beta function.

For each batch, the diffusion model's noise and denoising reconstruction objective remain unchanged; only the selection of $t$ is modified. This equips the model to devote more weight to gradient updates and error reduction during the late denoising stages that are empirically linked to detail reconstruction.

3. Comparative Analysis with Conventional and Contemporary Strategies

Standard Sampling

Standard approaches (uniform, logit-normal, or flat distributions as in SD3) do not differentiate between the constructive roles of early and late denoising. As a result, these models tend to underfit high-frequency contributions, leading to images that lack sharpness and intricate local structure. This is especially pronounced at very high spatial resolutions, where each denoising step must compensate for a rapid contraction of the solution manifold.

Other Detail-Oriented and Adaptive Schedules

DOTS is distinguished from heuristic or rule-based approaches by its parametric, easily tunable, and analyzable formulation. Related methods, such as adaptive non-uniform timestep sampling based on gradient variance (Kim et al., 15 Nov 2024), or importance-driven schedules for ODE-based solvers (Xue et al., 27 Feb 2024, Huang, 14 Dec 2024), provide different axes of adaptivity (objective-driven, error-bound minimization, etc.) and can be complementary or competitive depending on the operational regime.

In contrast with importance-driven adaptive selection (as in the Adaptive Sampling Scheduler (Wang et al., 16 Sep 2025)), DOTS is fully parametrized, model- and task-agnostic, and incurs negligible computational overhead, requiring no analytic analysis of SNR or gradient statistics.

Table: Comparison

Strategy	Sampling Focus	Implementation	Impact on Fine Detail
Uniform	All timesteps equally	Uniform random	Weak; oversmoothing
Logit-normal/flat	Mild center/late focus	Logit-normal distribution	Weak-moderate
DOTS (Beta)	Late, high-detail steps	$\mathrm{Beta}(\alpha<\beta)$	Strong; maximal FID_patch gains
Adaptive (e.g., importance or error)	Dynamically high-variance/importance steps	Analytic/objective-based	Moderate to strong, not always focused only on detail

4. Empirical Validation and Ablative Evidence

Extensive quantitative and qualitative studies on the UltraHR-100K dataset and UltraHR-eval4K benchmark demonstrate the significant benefit of DOTS for fine-grained detail synthesis:

• FID_patch, a regionally-sensitive version of FID, improves from 20.93 (baseline) to 15.79 (DOTS+SWFR).
• CLIP score remains high, indicating maintained semantic alignment.
• DOTS outperforms both uniform and alternative parametric (logit-normal, flattened) scheduling baselines with minimal change to core model structure.
• Ablation on Beta distribution skew parameters ($\alpha$,$\beta$) confirms that a moderate right skew ($\alpha=2$, $\beta=4$) yields maximal detail; over-skewing or insufficient skew degrade both detail and global metrics.

These findings confirm that strategically restructuring the distribution of update effort along the denoising timeline is crucial for achieving UHR-quality detail.

5. Integration with Model Architectures and Training Frameworks

DOTS is a modular, scheduler-level intervention. It does not require altering neural architectures, loss functions, or data augmentation routines. In the UltraHR-100K benchmarks, DOTS is combined with:

• Frequency spectrum regularization (SWFR), operating on the reconstructed images’ DFT coefficients to further encourage high-frequency fidelity.
• Standard backpropagation and loss formulations.
• Compatible with post-training adaptation and fine-tuning.

DOTS is strictly agnostic to image semantics, providing flexibility for a wide range of conditional or unconditional diffusion models targeting UHR or detail-critical domains.

6. Broader Context and Theoretical Justification

The principle underpinning DOTS is general: when the denoising trajectory is not uniform in its contribution to the target perceptual metric, scheduling learning pressure in accordance with contribution leads to improved resource allocation. DOTS explicitly realizes this via parametric biasing toward late (i.e., lower noise, detail-forming) steps, aligning well with empirical findings from spectrum analysis of denoising stages ([Yi et al., NeurIPS 2024]).

A plausible implication is that further gains could be achieved by integrating DOTS-style right-skewed sampling with schedule-adaptive, analytically optimized, or gradient-variance-based approaches, particularly in domains with known temporal inhomogeneity in information content.

7. Summary Table

Aspect	DOTS (Beta)	Standard Sampling
Timesteps focus	Right-skew ($t\to 0$)	Uniform or balanced
Goal	Maximize high-frequency detail	Semantic/balanced/efficient
Overhead	Minimal	Minimal
Applicability	Model/data-agnostic	Model/data-agnostic
FID_patch	Strong improvement	Weaker, oversmoothed
Implementation	Sample $t \sim \mathrm{Beta}$	Uniform/logit-normal/random

8. Conclusion

Detail-Oriented Timestep Sampling (DOTS) is a simple, effective, and data/model-agnostic training intervention for diffusion models. By parametric biasing of timestep sampling toward detail-forming denoising steps, DOTS enables state-of-the-art synthesis of fine-grained visual details in ultra-high-resolution text-to-image diffusion models, setting a new standard for plug-and-play scheduler-level training improvement. Consistent empirical and ablative results confirm that allocating more update steps to late denoising is essential for maximizing perceptual detail quality at scale (Zhao et al., 23 Oct 2025).