Not All Prediction Targets Keep Training-Free Diffusion Guidance on the Manifold¶

Conference: ECCV 2026
arXiv: 2607.00647
Code: https://github.com/ManLuML/on-manifold-tfg
Area: Diffusion Models
Keywords: Training-Free Guidance, Prediction Targets, Diffusion Models, Flow Matching, Manifold Preservation

TL;DR¶

This work theoretically proves that the prediction targets of diffusion models (\(\epsilon\)-prediction / \(v\)-prediction / \(x\)-prediction) form a strict error amplification hierarchy under training-free guidance (TFG). Specifically, \(\epsilon\)-prediction causes samples to drift off the data manifold in high-noise steps due to the divergence of the \(1/t\) factor in its reconstruction formula, whereas \(x\)-prediction directly outputs clean images without error amplification. These hierarchical effects are verified across three dimensions: a controlled crossed-lines ablation study, a 143-class fine-grained bird benchmark, and style transfer. Additionally, Child FID is introduced as a manifold-aware evaluation metric.

Background & Motivation¶

Training-free guidance (TFG) [DPS, LGD, FreeDoM, TFG] guides pre-trained diffusion models toward desired properties during inference using the gradients of a classifier or an energy function, without requiring retraining. Existing TFG methods generally rely on the clean image estimate \(\hat{x}\) to compute the guidance gradient \(\nabla_{z_t}\mathcal{E}(\hat{x})\): \(\epsilon\)-prediction (DiT) and \(v\)-prediction (SiT, PixelFlow) must reconstruct \(\hat{x}\) from the noisy state, whereas \(x\)-prediction (JiT) directly outputs the clean image.

However, strong guidance often drives samples off the data manifold, manifesting as catastrophic failures such as collapse and distortion. Traditional evaluation metrics, such as Validity (top-1 accuracy), fail to distinguish between genuinely generating target-class samples and generating adversarial perturbations that fool the classifier—a blind spot overlooked by 15 out of 17 TFG papers. When prior works maximized Validity under strong guidance, they unconsciously selected off-manifold images that merely fooled the classifier, rather than diverse samples belonging to the target class.

Key Challenge: The three prediction targets exhibit comparable generation quality (FID) but demonstrate fundamental differences in manifold preservation. The core issue is that the guidance quality of TFG depends on the accuracy of \(\hat{x}\)—when \(\hat{x}\) is inaccurate, the guidance gradient pushes samples off the manifold. Does the choice of prediction target dictate whether samples remain on-manifold under TFG? This paper answers in the affirmative through theoretical analysis (Propositions 1, 2, and Theorem 3.1) and systematic experiments.

Core Idea: The prediction targets induce a strict error amplification hierarchy via their reconstruction formulas: \(\epsilon\)-prediction diverges as \(t \to 0\), \(v\)-prediction decays boundedly, and \(x\)-prediction exhibits zero amplification. This makes \(x\)-prediction the most reliable foundation for training-free guidance.

Method¶

Overall Architecture¶

The research framework of this paper comprises three tiers: Theoretical Analysis (error amplification hierarchy and cumulative effects of the three prediction targets) \(\to\) Evaluation Protocol Design (Child FID + guidance scale Pareto sweep + fine-grained bird benchmark) \(\to\) Systematic Experimental Validation (crossed-lines controlled ablation \(\to\) ImageNet fine-grained guidance \(\to\) style transfer \(\to\) inverse problems). The input of the theoretical analysis consists of the reconstruction formulas of the three targets, and the output is a strict error amplification hierarchy and cumulative trajectory deviation upper bounds. The design motivation of the evaluation protocol is that existing Validity + FID metrics fail to detect manifold departure, yielding C-FID and guidance scale sweep curves as outputs. The experimental validation checks these theoretical predictions across multiple scales ranging from 2D toy datasets to ImageNet 256x256.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Three Prediction Targets<br/>eps / v / x-prediction"] --> B["Error Amplification Analysis<br/>Proposition 1: 1/t Divergence"]
    B --> C["Cumulative Trajectory Deviation<br/>Proposition 2: -ln(t0) Divergence"]
    C --> D["Gradient Stability<br/>Theorem 3.1"]
    D --> E["Manifold Force Interaction<br/>Remark 1"]
    E --> F["Child FID Evaluation Protocol"]
    F --> G1["Crossed-Lines Ablation"]
    F --> G2["Fine-grained Bird Guidance"]
    F --> G3["Style Transfer / Inverse Problems"]

Key Designs¶

1. Error Amplification Hierarchy of Prediction Targets (Proposition 1): Revealing \(1/t\) Divergence from Reconstruction Formulas

Under the Flow Matching framework, the noising process is defined as \(z_t = t \cdot x + (1-t) \cdot \epsilon\) (where \(t=0\) is pure noise and \(t=1\) is clean data). The three prediction targets reconstruct the clean image estimate \(\hat{x}\) through different formulations: - \(\epsilon\)-prediction: \(\hat{x}^{(\epsilon)} = (z_t - (1-t)\epsilon_\theta)/t\) - \(v\)-prediction: \(\hat{x}^{(v)} = z_t + (1-t)v_\theta\) - \(x\)-prediction: \(\hat{x}^{(x)} = x_\theta\)

\[\|\hat{x}^{(\epsilon)} - x\|_2 = \frac{1-t}{t}\delta_\epsilon,\quad \|\hat{x}^{(v)} - x\|_2 = (1-t)\delta_v,\quad \|\hat{x}^{(x)} - x\|_2 = \delta_x\]

As \(t \to 0\) (early steps with high noise), the error amplification factor \((1-t)/t\) of \(\epsilon\)-prediction diverges to infinity (\(\to \infty\)), whereas that of \(v\)-prediction, \((1-t)\), remains bounded, and \(x\)-prediction suffers no amplification. More importantly, the base prediction error itself scales with dimension: \(\delta_\epsilon \sim \sqrt{D}\) (as \(\epsilon\)-prediction must resolve all \(D\) dimensions of the ambient noise) versus \(\delta_x \sim \sqrt{d}\) (as \(x\)-prediction only maps onto the \(d \ll D\) dimensional manifold). For ImageNet (\(D=196,608\), \(d \approx 26-43\)), the base error alone exhibits an approximate \(68-87\times\) discrepancy, which is further exacerbated after factoring in the \((1-t)/t\) amplification.

2. Cumulative Trajectory Deviation (Proposition 2) and Manifold Force Interaction (Remark 1): Why Early High-Noise Steps are Fatal

Proposition 1 yields single-step error bounds, but guided sampling is a multi-step iterative process and the error at step \(k\) corrupts the state at step \(k+1\). Under a Lipschitz guidance energy \(\mathcal{E}\) for \(N\)-step uniform Euler sampling, the cumulative perturbation is bounded by:

\[C_\epsilon = \alpha L_g \int_{t_0}^{1} \frac{1-t}{t} \delta_\epsilon(t) dt,\quad C_v = \alpha L_g \int_{t_0}^{1} (1-t) \delta_v(t) dt,\quad C_x = \alpha L_g \int_{t_0}^{1} \delta_x(t) dt\]

Under the assumption of approximately constant base errors: \(C_\epsilon = \alpha L_g \delta_\epsilon[(t_0-1) - \ln t_0]\) (which diverges when \(t_0 \to 0\)), \(C_v = \alpha L_g \delta_v(1-t_0)^2/2\) (quadratic convergence), and \(C_x = \alpha L_g \delta_x(1-t_0)\) (linear convergence). These three distinct convergence behaviors directly dictate the guidance quality: high-noise steps near \(t_0 \to 0\) contribute the vast majority of the error in \(\epsilon\)-prediction, yet these early steps are precisely what determines the global structure of the sample—leaving the manifold at this phase prevents recovery, regardless of the manifold restoring force in subsequent steps.

Remark 1 further explains this phenomenon from the perspective of Score decomposition: the Score \(\nabla_{z_t}\log p_t(z_t)\) can be decomposed into a denoising component and a manifold restoring force. The latter is strongest when \(t \approx 0\) (diverging as \(\Theta(1/(1-t)^2)\)) and weakest when \(t=0\) (\(\approx 1\)). The \(\mathcal{O}(1/t)\) error amplification of \(\epsilon\)-prediction is strongest precisely when the manifold restoring force is weakest, allowing the guidance gradient to overwhelm the weak manifold force and push the sample off the manifold. \(x\)-prediction is free of this singularity, guaranteeing a stable combination of guidance and manifold forces.

3. Child FID and Manifold-Aware Evaluation Protocol: Distinguishing "Genuine Success" from "Fooling the Classifier"

Existing TFG evaluation protocols possess fundamental flaws: Validity (classifier top-1 accuracy) accepts any sample labeled by the classifier as the target class, including off-manifold artifacts—similar to how adversarial perturbations [Stutz et al.] easily trick classifiers. Parent FID (P-FID, using the entire ImageNet as the reference distribution) is equally unreliable: when guidance successfully narrows the generative distribution from a parent class to a specific subclass, P-FID increases due to reference distribution mismatch, regardless of the true sample quality.

This paper proposes Child FID (C-FID): using the target categories (a fine-grained bird dataset) instead of the entire ImageNet as the FID reference distribution. When guidance is successful, C-FID decreases (the generated distribution approaches the true distribution of the target class); conversely, when the guidance drifts off-manifold, C-FID increases (indicating that although the generated distribution fools the classifier, it remains distant from the true target class in the feature space). Combined with a Pareto sweep curve of guidance scale \(\rho\) (P-FID vs. C-FID), C-FID reveals the complete quality-guidance trade-off that single-point comparisons fail to capture.

The experimental protocol also constructs a fine-grained bird classification benchmark: 143 species are filtered from a 525-species bird dataset and nested under 30 ImageNet parent classes (with 2 to 20 species per parent, averaging 4.8), forming a natural two-level conditioning scheme—CFG guides to the parent class, and DPS guides to the specific subspecies, with the guidance classifier decoupled from the evaluation classifier to prevent circular evaluation [Shen et al.]. The elegance of this design lies in the fact that bird categories already reside within the ImageNet label space, allowing the pre-trained model to generate them without domain shift. Furthermore, inter-species differences (such as plumage, beak shape, and eye markings) require semantic-level changes, maximizing the distinction between the classifier-fooling mode and the on-manifold guided mode.

A Concrete Example: Crossed-Lines from \(D=2\) to \(D=512\)¶

Taking the crossed-lines experiment as an example: the underlying manifold consists of two orthogonal 1D lines \(b=a\) (class 0) and \(b=-a\) (class 1) in \(\mathbb{R}^2\), corrupted with perpendicular Gaussian noise, and embedded into an ambient space of dimension \(D \in \{2,8,32,128,512\}\) through a column-orthogonal projection. For each \(D\), three residual MLPs with identical architectures, training configurations, and random seeds except for their prediction targets are trained. DPS (\(s=10\), 100 Euler steps) is used to guide the generation toward class 1 for 10,000 samples.

At \(D=2\), all three targets perform well (\(\epsilon\): 65.8%, \(v\): 96.2%, \(x\): 100% on the manifold).
At \(D=32\), \(\epsilon\)-prediction already starts to fail (58.5%), while \(v\)- and \(x\)-predictions remain robust.
At \(D=512\), the hierarchy is fully exposed: \(x\)-prediction retains 93.3% on-manifold accuracy, \(v\)-prediction drops to 21.5%, and \(\epsilon\)-prediction plummets to just 0.5%—where almost all samples collapse into off-manifold noise. This serves as empirical proof of Proposition 1 combined with the dimension-scaling effect (Appendix 0.A): the compounding of \(\delta_\epsilon \sim \sqrt{D}\) and the \(1/t\) factor drives guidance in high dimensions toward catastrophic failure.

Loss & Training¶

This paper does not train new models; all diffusion models utilize official pre-trained weights. The core of the theoretical analysis relies on direct algebraic derivations of the reconstruction formulas—obtaining error amplification factors without network training or fine-tuning. In guided experiments, DPS utilizes the classifier gradient \(\rho \nabla_{z_t} \log p(y|\hat{x})\). For \(x\)-prediction, it directly uses \(x_\theta(z_t,t)\) as \(\hat{x}\), bypassing the unstable reconstruction formulas. Latent space models (DiT, SiT) require VAE decoding at each step to obtain pixel-space gradients, which increases computational overhead and reconstruction error.

Key Experimental Results¶

Main Results¶

Table 1 presents the key metrics of various models under DPS guidance (\(\rho=0\) represents the CFG-only baseline). The best results are selected based on the optimal C-FID under the premise that P-FID does not degrade significantly.

Model	Prediction Target	Space	\(\rho\)	P-FID \(\downarrow\)	C-FID \(\downarrow\)	Validity(%) \(\uparrow\)
DiT-XL/2	\(\epsilon\)	Latent	0	5.52	42.81	14.13
DiT-XL/2	\(\epsilon\)	Latent	0.10	6.70	38.11	26.69
DiT-XL/2	\(\epsilon\)	Latent	0.50	14.22	36.66	29.63
SiT-XL/2	\(v\)	Latent	0	5.07	41.58	13.68
SiT-XL/2	\(v\)	Latent	1.00	8.21	34.66	26.64
SiT-XL/2	\(v\)	Latent	2.00	12.48	34.94	27.61
PixelFlow	\(v\)	Pixel	0	6.29	44.07	13.55
PixelFlow	\(v\)	Pixel	2.00	11.69	36.22	20.13
PixelFlow	\(v\)	Pixel	5.00	28.24	47.71	18.07
JiT-B/16	\(x\)	Pixel	0	8.84	46.43	14.94
JiT-B/16	\(x\)	Pixel	6.00	12.24	31.30	26.77
JiT-H/16	\(x\)	Pixel	0	5.48	40.98	14.01
JiT-H/16	\(x\)	Pixel	3.00	6.91	32.85	26.60
JiT-H/16	\(x\)	Pixel	8.00	12.21	30.63	26.02

Key Observations: (1) At a matched Validity of \(\approx 26.6\%\), JiT-H yields a C-FID of 32.9 compared to DiT's 38.1, showing a gap of 5.2 points—a quality difference concealed entirely by traditional Validity metrics. (2) PixelFlow's C-FID improves under weak guidance (44.1 \(\to\) 36.2, \(\rho=2\)) but degrades to 47.71 under strong guidance (\(\rho=5\)), where this C-FID reversal acts as a direct indicator of manifold departure. (3) Larger models in the JiT family (B \(\to\) L \(\to\) H) achieve strictly superior Pareto frontiers: a guidance scaling effect exists, where model capacity enhances both generation quality and guidance responsiveness.

Ablation Study¶

Table 2 presents the manifold preservation rates of the three prediction targets across different ambient dimensions in the crossed-lines experiment (\(s=10\), 100 steps).

Target	\(D=2\)	\(D=8\)	\(D=32\)	\(D=128\)	\(D=512\)
\(\epsilon\)-prediction	65.8%	76.7%	58.5%	9.1%	0.5%
\(v\)-prediction	96.2%	97.5%	91.9%	43.7%	21.5%
\(x\)-prediction	100%	99.9%	100%	72.4%	93.3%

The dimension-scaling effect is prominent: \(\epsilon\)-prediction collapses from 58.5% at \(D=32\) to 0.5% at \(D=512\), validating the theoretical prediction of compounding \(\delta_\epsilon \sim \sqrt{D}\) and the \(1/t\) factor. The minor decline in \(x\)-prediction (100% \(\to\) 93.3%) stems primarily from the degradation of the classifier's guidance signal in high dimensions, rather than manifold departure.

Model Capacity Inversion Comparison: JiT-B/16 (\(x\), 131M) achieves a best C-FID of 31.3, outperforming DiT-XL/2 (\(\epsilon\), 675M) at 36.7 and SiT-XL/2 (\(v\), 675M) at 34.4. Winning despite being 5.2\(\times\) smaller in parameter size excludes model capacity as the primary explanation for \(x\)-prediction's superiority.

Key Findings¶

Mode Collapse Signature of \(\epsilon\)-prediction: DiT yields the highest DINOv2 Precision (0.24) but the lowest Recall (\(\sim 0.49\)). The combination of high Precision and low Recall acts as a textbook signature of mode collapse, indicating that \(\epsilon\)-prediction concentrates samples on a few classifier-friendly templates rather than covering the diverse natural variations of the target class. In contrast, JiT-H achieves a Recall of 0.59 with a Precision of only 0.17-0.19, sacrificing single-sample sharpness for genuine diversity.
Prediction Target > Operating Space: The comparison between PixelFlow (\(v\), pixel space) and JiT (\(x\), pixel space) directly decouples the operating space. Despite both operating in pixel space, PixelFlow exhibits a C-FID reversal (increasing to 47.7) under strong guidance, whereas JiT-H continues to decline to 30.6. This underscores that the choice of prediction target is the primary factor governing guidance robustness.
Stability Discrepancy under Guidance Scales: \(\epsilon\)-prediction reaches its optimal C-FID at \(\rho=0.1\); beyond this, while Validity increases, C-FID stagnates and P-FID skyrockets—a typical signal of a misallocated budget. The beneficial guidance scale range of \(x\)-prediction is roughly 16\(\times\) wider (yielding gains from \(\rho=0.5 \to 8\)), whereas the usable range for \(\epsilon\)-prediction is extremely narrow (\(\rho=0.05 \to 0.1\)).

Highlights & Insights¶

Reconstruction Formula as a Unified Explanatory Framework: The distinct behaviors of the three targets are traced back to a simple algebraic fact: whether the reconstruction formula contains a division by \(t\). This insight unifies seemingly unrelated observations (dimension-scaling issues in \(\epsilon\)-prediction training [Karras, Jin] and manifold departure under guidance) into a single, elegant causal chain.
Novelty of Child FID as a Manifold-Aware Metric: While FID is not a new metric, shifting the reference distribution from the full ImageNet dataset to specific target subclasses, paired with a guidance scale Pareto sweep, enables manifold-aware evaluation at negligible cost (requiring only a change in reference distribution without supplementary models). This evaluation protocol is immediately applicable to any ImageNet-scale diffusion model.
"Graceful vs. Catastrophic Failure" Decision Perspective: Achieving lower Validity while preserving image quality (JiT-H under strong guidance) is preferable to higher Validity coupled with collapsed diversity (DiT under strong guidance). In practice, users can retry generation to hit the target class but cannot recover from mode collapse or manifold departure. This practical insight fundamentally reorders evaluation priorities for TFG methods.
The "Free Lunch" of \(x\)-prediction in Guidance: Without requiring external counter-measures (such as Monte Carlo smoothing, iterative corrections, or repeated sampling), \(x\)-prediction achieves more stable guidance gradients purely through the inherent mathematical properties of its prediction target. This represents a non-trivial extension of JiT—while JiT established the manifold benefits during training, this work proves that this advantage persists and is equally prominent during inference-time guidance.

Limitations & Future Work¶

Imperfect Isolation of Model Architectures: When comparing \(\epsilon\)-prediction and \(x\)-prediction, DiT (latent space) and JiT (pixel space) carry differences in architecture and operating spaces. The authors candidly acknowledge this, relying on five independent lines of controlled experiments to establish convergence (crossed-lines full control, Latent-space matched DiT vs. SiT, JiT-B capacity inversion, PixelFlow C-FID reversal, and consistent task ranking) rather than a single "perfect" baseline comparison. Moreover, training an \(\epsilon\)-prediction model in ImageNet pixel space is practically unfeasible (exhibiting a 43\(\times\) performance gap of 372 vs. 8.62 FID), which itself serves as supporting evidence for the core thesis.
Simplifying Theoretical Assumptions: The theoretical analysis assumes Lipschitz energy functions and fully trained models, which may not hold perfectly in practice. Although the derived threshold ratio for guidance scales (\(\rho_x^*/\rho_\epsilon^* \approx 20\)) aligns with the experimental ratio (JiT \(\rho=8\) vs. DiT \(\rho=0.5\), a 16\(\times\) difference), there remains a slight gap in magnitude due to architectural and operating space discrepancies.
Restriction to Gradient-Based TFG Methods: Gradient-based methods such as DPS, LGD, FreeDoM, TFG, and Flow Guidance fall within the scope of the analyzed error amplification hierarchy. However, attention-perturbation methods (e.g., SAG, PAG, NAG, SEG) do not bypass \(\hat{x}\) through its gradient and are thus excluded from this analysis. The potential advantage of \(x\)-prediction in attention-based methods warrants independent study.
256x256 Resolution Limitation: All experiments were conducted at a 256x256 resolution. Under higher resolutions, the ambient dimension \(D\) increases (\(256^2 \cdot 3 = 196,608 \to 512^2 \cdot 3 = 786,432\)). According to the dimension-scaling analysis, the gap between \(\epsilon\)-prediction and \(x\)-prediction is expected to expand further, though empirical confirmation is required.
Future Work: Inference-time scaling techniques (such as DAS or inference-time search) heavily depend on the quality of \(\hat{x}\), where \(x\)-prediction should yield significant advantages in sample efficiency. Additionally, error accumulates across frames in video and text-to-image generation, potentially magnifying the performance gaps across different prediction targets.

vs Karras et al. EDM / Hang et al. MinSNR / Jin & Wang KDiff: These works characterize error amplification and dimension dependency of \(\epsilon\)-prediction from a training perspective. This paper's core contribution is extending these training-time observations to inference-time guidance, demonstrating that the prediction target affects guidance quality via the same mathematical mechanism (the reconstruction formula) but manifests in different ways (manifold departure vs. training instability).
vs Pidstrigach et al. Manifold Force Decomposition: Their Score decomposition splits the score into a denoising component and a manifold restoring force. Remark 1 of this paper directly leverages this framework, pointing out that the \(1/t\) amplification of \(\epsilon\)-prediction falls precisely in the high-noise region where the manifold force is weakest. These two independent theoretical threads converge here to provide a complete causal explanation for the experimental observations.
vs Shen et al. TFG Understanding: They first revealed the presence of adversarial gradients and the circular evaluation issue in TFG. This paper advances two steps further: (1) tracing the root cause of adversarial gradients back to the prediction target itself (due to the Jacobian of the reconstruction formula containing a \(1/t\) factor), rather than just the coupling of the guidance and evaluation classifiers; and (2) proposing C-FID as an actionable solution.
vs Li & He JiT: JiT serves as the foundational work proving the superiority of \(x\)-prediction during training. This paper is its natural extension—generalizing "manifold preservation during training" to "manifold preservation under inference-time guidance," proving that this advantage is not an accidental byproduct of training but is directly determined by the same error amplification hierarchy.

Rating¶

Novelty: ⭐⭐⭐⭐⭐ Connects the prediction target to TFG manifold preservation for first time. The theoretical framework (Propositions 1, 2, and Theorem 3.1) and systematic experimental design are entirely original. Child FID, acting as a manifold-aware evaluation metric, effectively resolves a ubiquitous blind spot shared by 17 previous papers.
Experimental Thoroughness: ⭐⭐⭐⭐⭐ The experimental design is exemplary: featuring a fully controlled crossed-lines ablation study, multi-scale sweeps on six ImageNet models, style transfer, inverse problems (deblurring + super-resolution), generalization validations on a butterfly domain, LGD/FreeDoM cross-method validation, and a model capacity inversion baseline. Each experimental vector systematically addresses a potential confounding explanation.
Writing Quality: ⭐⭐⭐⭐ The technical derivations are clear (direct algebraic substitution of reconstruction formulas \(\to\) Proposition 1 \(\to\) cumulative integral \(\to\) Theorem 3.1), and the experimental exposition is highly logical. The appendix's discussion of architectural discrepancies ("confounder as evidence") is candid and persuasive. A slight improvement could have been made in Section 3.3 by providing a more detailed account of the concrete algorithmic steps in TFG.
Value: ⭐⭐⭐⭐⭐ The conclusions offer direct practical guidance: practitioners building inference-time control pipelines should prioritize \(x\)-prediction models. For \(\epsilon\)-prediction models, this paper implies that strong guidance should be accompanied by additional manifold-constraint regularizations (such as Monte Carlo sampling in TFG or iterative corrections), though the \(1/t\) amplification inherent to \(\epsilon\) defines the upper limit of these mitigation strategies.

Complete Experimental Data Index¶

Fine-Grained Bird Guidance: The complete \(\rho\)-sweep data is available in the original paper's Table 6, covering DiT (\(\rho \in \{0, 0.05, 0.1, 0.25, 0.5\}\)), SiT (\(\rho \in \{0, 0.05, 0.1, 0.25, 0.5, 1, 1.5, 2\}\)), PixelFlow (\(\rho \in \{0, 0.5, 2, 3, 5\}\)), and the three JiT-B/L/H families with 5–9 distinct \(\rho\) scales each.
Crossed-Lines Complete Metrics: Table 10 provides manifold preservation rates, Target MMD, and classification accuracy across all dimensions (2/8/32/128/512). Semi-circle expansion experiments can be found in Table 11 and Table 12.
Style Transfer Complete Data: Table 7 covers Gram Distance and Content Accuracy for all six models (DiT/SiT/PixelFlow/JiT-B/L/H) across a \(\rho\) range of 0 to 50.
Inverse Problems Complete Data: Table 8 (Gaussian deblurring) and Table 9 (4x super-resolution) provide complete LPIPS/PSNR/SSIM scans for all six models.
Survey on Evaluation Habits: Appendix 0.D aggregates three tables detailing a comprehensive comparison of 17 TFG papers across three axes: FID sample size, manifold-aware evaluation metrics, and guidance scale sweeps.