arxiv: 2604.26503 · v1 · submitted 2026-04-29 · 💻 cs.CV

Recognition: unknown

Delta Score Matters! Spatial Adaptive Multi Guidance in Diffusion Models

Haosen Li , Wenshuo Chen , Lei Wang , Shaofeng Liang , Bowen Tian , Soning Lai , Yutao Yue

Authors on Pith no claims yet

Pith reviewed 2026-05-07 11:02 UTC · model grok-4.3

classification 💻 cs.CV

keywords diffusion modelsclassifier-free guidanceadaptive guidanceimage generationvideo generationdata manifolddetail-artifact dilemma

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The pith

Point-wise adaptive guidance scales resolve the detail-artifact trade-off in diffusion models.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Standard classifier-free guidance applies one fixed scale across every pixel or frame, so low values miss fine semantic details while high values create over-saturation, structural breaks, and video flicker. The paper traces the root cause to the fact that this uniform scale performs a straight-line extrapolation on a curved data manifold, pushing samples off the manifold in the orthogonal direction. SAMG measures a local conditional guidance energy at each point, then applies a low scale only where energy is high (near boundaries and textures) to stay safe and a high scale where energy is low to push semantics harder. The method is training-free and adds essentially zero cost. Experiments on image and video diffusion models show clearer semantics, preserved structure, and smoother motion.

Core claim

CFG performs a tangential linear extrapolation on the curved natural data manifold; the resulting orthogonal deviation is the source of the detail-artifact dilemma. SAMG derives a geometric upper bound on guidance and replaces the global scalar with point-wise conditional guidance energy, applying the conservative minimum scale at high-energy boundary regions to protect micro-textures and the aggressive maximum scale at low-energy regions to maximize semantic injection.

What carries the argument

Point-wise conditional guidance energy that selects between minimum and maximum guidance scales at each location so the sampling trajectory remains bounded on the data manifold.

Load-bearing premise

The point-wise conditional guidance energy correctly flags which regions need conservative versus aggressive scales, and the derived geometric upper bound actually keeps the trajectory on the manifold.

What would settle it

Generate the same prompts with and without SAMG on a fixed diffusion model, then measure whether SAMG fails to improve (or worsens) both semantic alignment scores and structural/temporal artifact metrics.

Figures

Figures reproduced from arXiv: 2604.26503 by Bowen Tian, Haosen Li, Lei Wang, Shaofeng Liang, Soning Lai, Wenshuo Chen, Yutao Yue.

**Figure 1.** Figure 1: Visualizing the “detail-artifact dilemma” in Classifier-Free Guidance and our solution. view at source ↗

**Figure 2.** Figure 2: Qualitative comparison of Conditional generation, High CFG, and SAMG. Prompt: “close view at source ↗

**Figure 3.** Figure 3: Visualization of the generated image and the evolution of spatial guidance energy maps view at source ↗

**Figure 4.** Figure 4: Qualitative comparison of video generation. view at source ↗

**Figure 5.** Figure 5: Visualization of decoupled latent energy evolution across the four SDXL channels. view at source ↗

**Figure 6.** Figure 6: A limitation of SAMG in handling dense semantic overlaps. view at source ↗

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

SAMG gives a practical spatially varying guidance rule that might help the detail-artifact issue, but the claimed geometric derivation does not appear to justify the specific energy-based scaling.

read the letter

The main point is that the authors take the known problem with uniform classifier-free guidance and try to fix it with a spatially adaptive scale that uses local conditional guidance energy to choose between min and max values at each pixel. They frame CFG as a tangential linear step on a curved data manifold via Tweedie's formula and differential geometry, then introduce SAMG as a training-free way to apply conservative scales where energy is high and aggressive ones where it is low. That framing and the zero-overhead implementation are the concrete new pieces. If the experiments on SD 1.5, SDXL, SD3.5, CogVideoX and ModelScope actually show better semantic alignment and temporal smoothness without extra cost, the method itself could be worth trying in practice. The soft spot is exactly where the stress-test note flags it: the paper moves from the geometric upper bound to the point-wise energy rule without a visible inequality or derivation that ties the two together. The energy looks like a normalized difference of conditional and unconditional scores, which is a reasonable heuristic but not obviously the quantity that respects the manifold bound they derive. Without those steps the theoretical justification is weaker than presented. The rest of the paper looks like standard CFG literature plus the new algorithm, with no obvious circularity in the reported results. This is for people who implement or tune diffusion sampling and want a lightweight adaptive trick. A reader who cares about practical improvements to guidance would get value from the method description and the reported qualitative gains even if the geometry story needs tightening. I would send it to peer review because the idea is concrete, the claims are falsifiable, and the experiments span multiple models.

Referee Report

3 major / 2 minor

Summary. The paper claims that Classifier-Free Guidance (CFG) in diffusion models performs tangential linear extrapolation on a curved data manifold (via Tweedie's formula), causing orthogonal deviations that manifest as the detail-artifact dilemma. It derives a theoretical upper bound on guidance scales from differential geometry to keep trajectories bounded, then introduces Spatial Adaptive Multi Guidance (SAMG): a training-free sampler that computes point-wise conditional guidance energy and applies conservative (min) scales to high-energy regions while using aggressive (max) scales in low-energy regions. Experiments on image (SD 1.5/ XL/ 3.5) and video (CogVideoX, ModelScope) models reportedly show improved semantic alignment, structure, and temporal consistency at no extra cost.

Significance. If the geometric upper bound is rigorously derived and the adaptive energy rule is shown to respect it, SAMG would offer a principled, zero-overhead improvement to a core sampling technique used across generative vision. The training-free nature and multi-architecture validation are strengths; a sound manifold-based justification could influence guidance design beyond ad-hoc scaling.

major comments (3)

[§3] §3 (geometric analysis): The upper bound on orthogonal deviation is derived from the curvature of the data manifold and Tweedie's formula, but the subsequent definition of 'conditional guidance energy' (used to decide min vs. max scale per pixel) is not shown to be bounded by or equivalent to this quantity. The energy appears to be an empirical score difference without an explicit inequality linking it to the manifold deviation bound, so the claim that SAMG 'keeps trajectories safely bounded' rests on an unverified identification rather than a proven relation.
[§4.1] §4.1 (SAMG algorithm): The adaptive rule applies min_scale to high-energy boundary regions and max_scale to low-energy regions, yet no ablation or sensitivity analysis is provided on how the energy threshold or the specific min/max values (free parameters) affect the bound; if the energy is not monotonically related to deviation magnitude, the rule could violate the theoretical upper bound in some regions.
[Experiments] Experiments section: While qualitative and quantitative results are reported across SD 1.5, SDXL, SD3.5, CogVideoX and ModelScope, the paper does not include a direct comparison of the proposed energy against alternative proxies (e.g., gradient magnitude or reconstruction error) to confirm it is the correct indicator of required scale; without this, superiority over uniform CFG or other adaptive baselines may be overstated.

minor comments (2)

[§4] Notation for the conditional guidance energy should be introduced with an explicit equation number and its normalization clarified (e.g., whether it is L2-normed or per-channel).
[Abstract] The abstract states 'virtually zero-cost' but the method requires an extra forward pass for the unconditional score at each step; clarify the exact overhead relative to standard CFG.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments identify important areas where the connection between the geometric analysis and the SAMG algorithm can be made more rigorous, and where additional experimental validation would strengthen the claims. We address each major comment point by point below and will revise the manuscript to incorporate the suggested clarifications and analyses.

read point-by-point responses

Referee: [§3] §3 (geometric analysis): The upper bound on orthogonal deviation is derived from the curvature of the data manifold and Tweedie's formula, but the subsequent definition of 'conditional guidance energy' (used to decide min vs. max scale per pixel) is not shown to be bounded by or equivalent to this quantity. The energy appears to be an empirical score difference without an explicit inequality linking it to the manifold deviation bound, so the claim that SAMG 'keeps trajectories safely bounded' rests on an unverified identification rather than a proven relation.

Authors: We appreciate the referee's precise identification of this gap. Section 3 derives the upper bound on orthogonal deviation from the curvature term in the local approximation of Tweedie's formula and shows that uniform CFG produces deviations orthogonal to the manifold. The conditional guidance energy is introduced as the point-wise score difference, which is the quantity that drives the orthogonal component under the same local linearization. While the manuscript presents this as a direct link, we acknowledge that an explicit inequality establishing that the energy is bounded by (or proportional to) the curvature-derived deviation term was not formally stated. In the revision we will add a short derivation in §3 showing that, under the first-order approximation used for the bound, the energy is monotonically related to the deviation magnitude, thereby justifying that conservative scaling in high-energy regions keeps trajectories within the derived bound. revision: yes
Referee: [§4.1] §4.1 (SAMG algorithm): The adaptive rule applies min_scale to high-energy boundary regions and max_scale to low-energy regions, yet no ablation or sensitivity analysis is provided on how the energy threshold or the specific min/max values (free parameters) affect the bound; if the energy is not monotonically related to deviation magnitude, the rule could violate the theoretical upper bound in some regions.

Authors: We agree that the absence of sensitivity analysis leaves the robustness of the min/max rule open to question. The design choice (min scale on high-energy regions, max on low-energy) follows from the geometric observation that high-energy locations are where the orthogonal deviation is largest. To address the concern directly, the revised manuscript will include an ablation subsection in §4.1 that (i) varies the energy threshold and the concrete min/max values over a range, (ii) reports the resulting deviation metrics on both synthetic curved manifolds and real diffusion trajectories, and (iii) verifies that the chosen rule never exceeds the theoretical upper bound derived in §3. We will also add a brief monotonicity check (empirical correlation between energy and measured deviation) to confirm the rule does not inadvertently violate the bound. revision: yes
Referee: [Experiments] Experiments section: While qualitative and quantitative results are reported across SD 1.5, SDXL, SD3.5, CogVideoX and ModelScope, the paper does not include a direct comparison of the proposed energy against alternative proxies (e.g., gradient magnitude or reconstruction error) to confirm it is the correct indicator of required scale; without this, superiority over uniform CFG or other adaptive baselines may be overstated.

Authors: We accept that a direct comparison of the conditional guidance energy against other candidate proxies would provide stronger evidence that it is the most appropriate indicator. The current experiments demonstrate consistent gains over uniform CFG and several published adaptive baselines, but they do not benchmark the energy metric itself against alternatives such as gradient magnitude or reconstruction error. In the revised version we will add a targeted comparison in the Experiments section: for each model we will compute three proxies (our energy, gradient magnitude, and reconstruction error), apply the same min/max adaptive rule with each proxy, and report both quantitative metrics (FID, CLIP score, temporal consistency) and qualitative examples. This will allow readers to see which proxy best correlates with reduced artifacts while preserving semantic alignment. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's chain proceeds from a standard reference (Tweedie's formula) to an interpretive geometric analysis of CFG as tangential extrapolation, followed by formulation of a theoretical upper bound on orthogonal deviation and a heuristic adaptive rule (point-wise conditional guidance energy) that applies min/max scales spatially. No equation is shown to equal a fitted input by construction, no load-bearing premise reduces to a self-citation whose validity depends on the present work, and the proposed SAMG algorithm is presented as a training-free heuristic motivated by the geometric insight rather than a statistical prediction forced by data reuse. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on a geometric reinterpretation of CFG and an unverified upper bound; no independent evidence or shipped code is supplied in the abstract.

free parameters (2)

min_scale
Conservative guidance scale applied to high-energy boundary regions; value not specified in abstract.
max_scale
Aggressive guidance scale applied to low-energy regions; value not specified in abstract.

axioms (1)

domain assumption CFG performs tangential linear extrapolation on a highly curved natural data manifold
Invoked via analysis of Tweedie's Formula in the abstract.

pith-pipeline@v0.9.0 · 5583 in / 1278 out tokens · 66517 ms · 2026-05-07T11:02:21.220036+00:00 · methodology

discussion (0)

Forward citations

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