Rectified CFG++ for Flow Based Models
Authors: Shreshth Saini
Shashank Gupta
Alan Bovik
Venue: NeurIPS 2025 poster ()
Keywords: Quality
Perceptual
Generation
T2I
Guidance
Sampling
Primary area: deep_learning
TL;DR: We propose a new guidance method for flow based models for better sampling and generation quality.

Abstract: Classifier‑free guidance (CFG) is the workhorse for steering large diffusion models toward text‑conditioned targets, yet its naïve application to rectified flow (RF) based models provokes severe off–manifold drift, yielding visual artifacts, text misalignment, and brittle behaviour. We present Rectified-CFG++, an adaptive predictor–corrector guidance that couples the deterministic efficiency of rectified flows with a geometry‑aware conditioning rule. Each inference step first executes a conditional RF update that anchors the sample near the learned transport path, then applies a weighted conditional correction that interpolates between conditional and unconditional velocity fields. We prove that the resulting velocity field is marginally consistent and that its trajectories remain within a bounded tubular neighbourhood of the data manifold, ensuring stability across a wide range of guidance strengths. Extensive experiments on large‑scale text‑to‑image models (Flux, Stable Diffusion 3/3.5, Lumina) show that Rectified-CFG++ consistently outperforms standard CFG on benchmark datasets such as MS‑COCO, LAION‑Aesthetic, and T2I‑CompBench. Project page: https://rectified-cfgpp.github.io/.

Rectified-CFG+ for Flow Based Models
Shreshth Saini
Shashank Gupta Alan C. Bovik
The University of Texas at Austin
{saini ahashank gupta)@utexeene edu
Vitx
CPG
Rectifled
Are-ar
Ma
Ree CPC
Visual outputs from Flux, w/ standard CFG, and w/ Reetified-CFG++ for Prompt: Kayak in the water, optical color, aerial view, rainbow. While CFG amplifies detail, it introduces artifacts such as oversaturation and structural distortion. Rectified-CFG+t produces semantically faithful results with improved alignment and texture realism. Bottom: A conceptual manifold view of sampling dynamics. (Left) Conditional and unconditional flows diverge across latent manifolds Mr. (Middle) CFG combines them by extrapolation, forcing the trajectory outside M, (blue path). (Right) Rectified-CHC CFG++ first steps along the conditional field then applies a scheduled interpolation towards the unconditional field, keeping the iterate inside the manifold family (green path) and thus avoiding artifacts while improving prompt alignment.
Figure 1: Top:
Abstract
Classifier-free guidance (CFG) is the workhhorse for steering large diffusion models toward text-conditioned targets, yet its naïve application to rectified flow (RF) based models provokes severe off-manifold drift, yielding visual artifacts, text misalignment, and brittle behaviour. We present Rectifie-CCFG+4 an adaptive predictor-corrector guidance that couples the deterministic efficiency of rectified flows with geometry-aware conditioning rule. Each inference step first executes a conditional RF update that anchors the sample near the learned transport path, then applies a weighted conditional correction that interpolates between conditional and unconditional velocity fields. We prove that the resulting velocity field is marginally consistent and that its trajectories remain within bounded tubular neighbourhood of the data manifold, ensuring stability across a wide range of guid- ance strengths. Extensive experiments on large-scal sange-scale text-to-image models (Flux, Stable Diffusion 3/3.5, Lumina) show that DectifiedCCFG-. consistently outper- forms standard CFG on benchmark datasets such as MS-COCO, LAION-Aesthetic, and BelcCh Project page: httts::/rectifiieee gpp. gi thub. io/.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

Introduction
Generative models have seen dramatic advances diffusion-based methods now achieve state-of-the- art image synthesis by learning to reverse a stochastic or deterministic noise process via SDES/ODEs [36, 12, 6, 34, 37, 4], combined with scalable architec- tures [28, 30] and fast samplers [24, 44] to far out- perform earlier GAN approaches [2]. More recently, rectified flow models [22, 21J dispense with stochas- ticity by learning deterministic vector fields reducing generation to an ODE solve yielding stable training and faster sampling than diffusion [9], and large-scale flow systems like SD3 [7] and Flux [1] outperform diffusion-quality images using a fewer function eval- uations.
CFG
CFG
CFG
Prompl: Inside steumpunk workshop, a young cute redhead...
Prompt: winter forest soowecovered
Figure 2: Effect of guidance on flow-based models. (Left) Unguided samples lack struc- ture; (Middle) naive CFG introduces semantic drift and artifacts. (Righr) Rectified CFG++ yields detailed and well-aligned outputs.
An essential advancement in diffusion models is classifier-free guidance (CFG) [13], which drastically enhances conditional generation quality and enables precise alignment of generated samples with textual prompts. CFG linearly extrapolates the unconditional
score toward the conditional score to sharpen adherence to the prompt, at the expense of potential instability and generation artifacts. Although CFG is simple and effective for stochastic diffusions, its extrapolative nature is problematic in deterministic flows [5]: the trajectory is pulled off the learned manifold, producing color blow-outs, warped geometry, and hyperparameter sensitivity (Fig. 2), thus limiting practical applicability. Subsequent variants variants-dynamic thresholding [34], Characteristic guidance [43]. CFG++ [5], and APG [33] have tried to alleviate these effects, in diffusion models, yct a principled, flow-specific solution remains missing.
To address these limitations, we introduce Rectified-CFG++ rectified-flow models. Our key insight is that the geometric structure of RF sampling favors in- terpolation, which synergistically combines the stable and deterministic generative trajectories of rectified flow models with the powerful conditional generation capabilities of classifier-free guidance. At every step, Recitified-CFG- transport path, then (ii) applies a scheduled interpolation towards the conditional and unconditional field previously obtained conditional samples. The resulting predictor corrector integrator (Sec. 3) preserves marginal consistency, maintains on on-manifold trajectories thereby effectively eliminating off-manifold artifacts, and requires no extra networks optimization. Morcover, we provide theoretical foundation for Rectified-CFG+ and show that it ensures the stability of generated sam- ples on the underlying data manifold. We explain the geometric interpretation of Rectified-CFOG and demonstrate how it maintains trajectories within the manifold, thereby preventing the detrimen- tal deviations common to CFG sampling. Extensive experiments four large text-to-image RF backbones-Flux [1]. Stabe--Diffusion 3/3.5 [7], and Lumina-Nex((66-shoo that Rectified CFG++ consistently outperforms vanilla CFG [13] across FID [11], CLIP-Score [27, 10, 15), ImageRe- ward [42], Aesthethic Score [35], and HPS-v2 [40], while reducing artifacts such as oversaturation and typographic failure (Sec. 4). We also conduct subjective study. Qualitative comparisons (Figs. and 3) reveal smoother intermediate states and sharply improved text alignment. Our contributions
guidance scheme tailored for
(i) follows the conditional RF field to keep the sample on the
predictor-corrector
are summarized as follows:
We propose Rectified-CFG- novel predictor-corrector sampler that uses time-scheduled interpolation between conditional and unconditional velocity fields. Our method is parameter-free beyond the guidance scale.
We provide a detailed theoretical justification including rigorous proofs, and a geometric interpreta- tion that our sampler preserves manifold consistency and superior conditioning efficacy.
Using diverse datasets and comparison against leading models, we demonstrate that Rectified- CFG++ yields better prompt alignment and visual quality than CFG, while mitigating its character- istic artifacts in flow- models.

---

Rect-CFG++
Prompt: A lome unthrepomopphic fox in crystalline wamurai amior standing still in a hamboo grove made of glass, glowing nanes etched into
Figure 3: Comparison of intermediate denoising steps of CFG and Rectified-CFG++. Visual progression of decoded latents across sampling steps, starting from 1=1000 (top left) to (-0 (top right). While CFG led to artifacts and structural instability early on, Rectified CFG++ maintained on-manifold transitions and preserved fine textures throughout.
By bridging the gap between fow-matching ODEs and modern guidance techniques, Reetified-CGG+ unlocks high-fidelit, manifold-awan awwre conditional generation with the efficiency benefits of rectified flows.
2 Preliminaries
We review (i) conditional flow-matching (CFM) for generative ODEs and (ii) classifier-free guidance (CFG) as typically used with diffusion/flow models. Throughout, x r Po denotes data sample, 20, I) Gaussian prior, and t E [0, is time index.
y + Rd that transports latent states from the prior pi to the data distribution po, conditioned on an input y y (e.g. text prompt):
Flow matching models: CFM [21, 22] learns velocity field Rd x [0,1] =
d = vo t, y),
(1)
dt
convenient probability path is the linear mixture pt = (1 (1-th t)pp + p1; drawing (ro. x1 ~ (po, P1) yields a floeed-frrm target velocity un (x)( 21 zo. Training minimises the conditional www-mathhing loss [21]:
LCFM (0) Fo (o t, v) (x (m)
where x, (1 2g + f.r, At inference we numerically integrate (1) deterministically. typically with an ordinary differential equation (ODE) Solver [37, 23]. The marginal velocity [21] required can be written as:
Uy (Ix) -rroro (xx
Classifier free guidance for flows: CFG [13] steers generation towards the condition by combining the conditional and unconditional velocity fields of single network trained with randomized null conditions Ø:
d (rt, 1, w) = (1 - w) no (Zt, 1, 2) + (o f, v):
where w >> 1 is the guidance scale that controls text-alignment strength. In (4), extrapolates guidance along Arς = ve ( l, y) no (2e. I, Ø), which often sends trajectories off the learned data manifold, producing oversaturated distorted images [5].
Notation: For brevity we write of == uo v).
320 = Uo(e,,
Au == of - o/.
Standard CFG updates 2, via the ODE step Ti-Ai 2, + At (o + wwe)), which is affine
extrapolation in Auf. While flow models offer deterministic, fast sampling, naively plugging (4) into the ODE solver inherits the same off- manifoll drift observed in diffusion models [5, 33), which can lead to divergence because the flow field is integrated without stochastic regularization effect of introduced noise in diffusion SDEs. These limitations motivate our Rectified-CFGG: strategy introduced in Sec. 3, which replaces the extrapolation term wArg with time-scheduled interpolation that preserves the geometry of the learned transport path.
3

---

3 Method
In the context of ODE integration, especially when the underlying vector field corresponds to transport along potentially curved manifolds,
Algorithm 1 Rectified-CFGi
Require: Velocity network 6a 6, y]: text prompt y. At: a(t)
Amax +37 with Amax 2 00772220 e e I"
applying Eq. (4) can lead to significant devia- tions from the true conditional paths learned by the model [5, 8, 331. This often results in vi- sual artifacts like oversaturation, semantic drift, and structural inconsistencies (see Fig. 2 and Fig. 3). To overcome these limitations, we pro- pose Rectified-CFG++ which is detailed in Al- gorithm 1. Our approach replaces the unstable extrapolation of CFG with an adaptive predictor- corrector that leverages the geometry of the learned conditional flow, while incorporating guidance in a controlled manner.
1: mg ~ (().T)
P prior sample P1
2: for
do
3:
"i vo(lee 1, v)
Conditional flow
4:
5, o - xe + At n//2
>
Predictor Optionally
5:
a o - 8,- - 3/ +
6:
vf Ar + vol2, (- -- A1/2, M)
7:
F A wolz, 4. A1/2, R)
8:
of (1(1)(; A -
Carrector
9: h ODEUpdate(#s;
Exe
D. ODE Update Step
10: end for
11: return 300
Generated Sample
3.1 Prctified-CFG+
The Rectified-FGG++ guidance modifies the velocity used within each step of a numerical ODE solver. Instead of directly using the CFG velocity Eq. (4), it constructs an effective velocity Ωx using information from both the current state 2a and a predicted future state, within time interval [t. t A//2].
Conditional Predictor: Specifically, use the conditional velocity of the predictor step. This
crucial because our goal is to generate sample following the condition y. Using of immediately steers the prediction towards the target subspace manifold MM. Using of or a CFG-mixed velocity here could introduce instability early in the step [33, 8].
T /t-21/2 + 24 + 2t/2(1().
(5)
Geometrically (Fig. 1(Middle)), the intermediate conditional update brings the sample along the manifold. This avoids going off-manifold early on in sampling, see Fig. 3.
Correction via Guidance Difference: Instead of averaging derivatives [3], following [13, 33,431]] we compute the difference between conditional and unconditional velocities in CFG [13], Ae". but at the intermediate predicted point. This term specifically isolates the signal related to the condition in the vicinity of where the trajectory is heading. Evaluating it at Æz-At/2 provides more relevant guidance correction as compared to using Ar, especially if the vector field rapidly changing speed or direction:
o A1/2 + -o(#x- At/2. A1/2 + uo (31 2))
Interpolative Update: The final effective velocity Ex anchors the update firmly to the current conditional direction of and adds correction based on the predicted guidance need, scaled by a weight term. This avoids using the unstable u²" as a base and replaces extrapolation with an adaptive correction based on intermediate prediction:
Ox + of + (V
-0 44
(8)
This structure aims to maintain proximity to the learned conditional flow path, while incorporating guidance information (Avξ- evaluated at a more relevant intermediate point, thereby enhancing stability and fidelity as compared to direct CFG [13] extrapolation.
3.2 Theoretical Analysis
Next we provide theoretical justification of the improved stability of Rectified-CFG-+ Let the (2) ly) denote the true trajectory under the ideal conditional velocity "ø( 4 y). generating the manifold M. = (1h, (x) [y) Æ ~ }- In the following, we say that the function f Lipschitz continuous on if f(a) f(b) < Lla b). Va, b e E, where L is a Lipschitz constant.
4

---

Table Comprehensive Quantitative Evaluation of CFG against Rectified-CFG+ when both are integrated into leading T2I Models on MS-COCO 10K validation samples. Lower(J) FID and higher(t) CLIP, Aesthetic, ImageReward, PickScore, and HPSv2 scores indicate better performance. Best values are highlighted in orange, and second best in gray.
Model
Guidance
FID
CLIP
Aesthetlc
RmageReward's
PlekScore f
HPSv2
Lumina [26]
CRG Rect-CFG++
26.9321
22.4899
0.3511
0,3464
5.8226
3.7755
0.9611
1,0924
D.5867
0.6133
0.3004
0.2797
SD3 [7]
CRG Rect-CFG++
23,8898
23,3945
0.3439
0,3471
5,5465
3.6529
0,9812
1.0009
0.4408
0.5891
0.2751
0,2897
SD3.5 [7]
CRG
Rect-CFG++
20.2169
20.2945
0.3506
0.3497
6,1651
6.155
1.0796
104877
0,5077
0.4925
0.2933
0.2946
Flux-dev [1]
Rect-CFG++
CRG
32.2262
37 86.8
0.3351
0,3493
4.7210
5.3251
0.9480
1.0528
0.3248
0.6752
0.2996
0.2621
Assumptions: (A1) (o f, y) and vo(ar, 2) are Lipschitz continuous in with constant L, and uniformly in continous / and y. (A2) The guidance direction magnitude is bounded: || | (x)] < B for all (x, y) E IR$, for some B R. (A3) The schedule a(t) is bounded and integrable. (A4) The conditional velocity magnitude is bounded: [[e](()]] I Vmax for all (a, (,,t,y) v) E R for some Vmaa R.
We begin by analyzing how the guidance term evaluated at an intermediate point relates to the guidance term the current point (f).
Lemma 3.1 (Stability of Predicted Guidance Direction). Under assumptions (Al) and (A4), the guidance direction Aet computed at the predicted state ēt-Dt/2 differs from the guidance direction Aut( (xx) at the current state by amount proportional the step size At:
|| - De (xx))l S LV mVmax
Proof. See Appendix A.2.
This lemma suggests that for sufficiently small step sizes, the guidance direction computed the predicted point 7 21/2 is close the direction at the current point Hı, thereby ensuring the correction term relevant. Next, we quantify the deviation introduced by the guidance correction in a single step, compared to following the pure conditional flow.
Proposition (Bounded Single-Step Perturbation). Let it-1 be the result of single Rectified- CFG++ step from σt. Let #,-1 1 be the result of a pure conditional Euler step. Under assumption (A2), the deviation is:
| - -,-11111 a(t)
Proof. See Appendix A.3.
This proposition implies that the per-step deviation from the conditional path is directly controlled by the weight (t) and the bound B imposed on the guidance field magnitude, scaled by the step size At. Thus, the Rectified-CGG+ trajectory stays within a bounded tubular neighborhood of the ideal manifold M, The size of this neighborhood is controlled by the guidance strength (t) and by the guidance field bound B. This analysis shows that, unlike standard CFG whose extrapolative nature lead divergence, the trajectories of Bectiied-CFG++ are anchored to Applying
controlled correction based on A A remains boundedly close to the target conditional flow path. This mathematical stability ensures to the empirical robustness and artifact reduction observed our results.
A1/2 with guidance weight att) ensures that the trajectory
Experiments
In this section, we present comprehensive empirical evaluation of Rectified-CFG+t for text-to- image (T2I) generation using large-scale models. Our experiments aim to rigorously demonstrate the effectiveness of our approach at improving text-image alignment, color fidelity, and the preservation of fine details, generating high-quality samples while expending comparable inference costs as competing baseline methods.
To provide multifaceted assessment of generated image quality and prompt adherence, we employed suite of established metrics. We measured perceptual image quality and
Evaluation Metries:
5

---

Table 2: Quantitative Evaluation T2I- CompBench. Evaluated across Color, Shape, Texture, and Spatial metrics. Rectified-CFG+ improves consistently across all dimensions.
Table 3: Quantitative Comparison of Guid- ance Strategies on MS-COCO IK. We eval- uated standard guidance methods against Rect- CFG++ using FID (J), CLIP (t), ImageReward (1), and HPSv2 (1) scores.
Model
Color
Shape
Texture
Spatial
Luminna [26]
0.7358
0.6898 0.7042
0.7365 0.6856
0.3586 0.3608
Guidance
FTD
ImageReward
CLIP
HPSv2 1
w/ Rect-CFG++
0.7767
SD3 [7]
0.7658
0.5698
0.7270
0.3199
SD3.5
77.3049
0.3852
0.3260
0.2421
w/ Rect-CFG++
0,8041
0,5778
0.7362
0.3306
w/
67,7133
1,0830
0,3515
0.2941
S133.5 [7]
0.7698
0,5792
0.7413
0.2856
w/ Rect-CFG++
0,7770
0.6014
0.7627
0.2909
w/ CFG-Zero"
68,3909
0.9947
0,3458
0.2879
w/ APG
67.2311
1,0748
0,3513
0.2935
Flux-dev [1]
0.6132
0,4152
0.5928
0.2488
w/ Rect-CFG++
0.7728
0,5018
0.6705
0.2790
w/ Reci-CFG++
67.1495
1,0845
0.3506
0.2959
realism using the Fréchet Inception Distance (FID) [11], and we quantified text-image semantic alignment is using CLIP-Score [27, 10, 15]. Furthermore, to capture aspects related to human preferences, visual aesthetics, and overall quality, we utilize ImageReward [42], PickScore [18, 38], HPSv2 [40], and Aesthetic Score [35]. These metrics collectively allow for a thorough evaluation of the generated images from different perspectives.
Datasets and Baselines: We conducted objective model comparison on standard T2I benchmark datasets. Specifically, we used subsets of the MS-COCO dataset [20, 5], comprising 10,000 and 1,000 image-text pairs (referred to as MS-COCO 10K and MS-COCO 1K, respectively). We also used a subset of 1,000 image-text pairs from LAION-Aesthetie [35] (LAION-Aesthetie 1K) and the 1,000 prompts from Pick-A-Pic [18]. To demonstrate the broad applicability of Rectified-CFG++ we integrated it into and evaluate it on several state-of-the-ar flow-based T21 foundation models: Stable Diffusion 3 [7]. Stable Diffusion 3.5 [7], Flux [1], and Lumina [26]. These models are representative of current advancements in flow-based generative architectures.
Implementation Details: All experiments were performed using a single NVIDIA A100 40GB GPU, When using our proposed method, Rectified-FG+++ we determined of effective hyperparameters which were kept consistent across all datasets and when integrated into baseline models. For all the compared methods, we utilized the default settings and configurations as reported in their original publications to ensure fair comparisons. Further detailed information regarding the experimental setup and hyperparameter settings can be found in Appendix D.1.
4.1 Text-to-Image Generation Evaluation
4.1.1 Quantitative Evaluation
We first assess performance using established quantitative metries. Table 3 provides a comparison on MS-COCO-I 1K against several guidance strategies: standard CFG [13], CFG++ [5], APG [33], and CFG-Zero* [8]. Rectified-CFG-+ consistently outperformed the other strategies across all
metrics on $D3.5 [7]. The results of a more comprehensive evaluation across multiple foundation models on MS-COCO-I0R are given in Table 1. These outcomes clearly demonstrate the efficacy of using Rectified-FGG+ when combined with leading text-to-image models. As compared to standard CFG integrated with the same base models, our method consistently improves scores across nearly all metrics. Notably, Rectified-CFG+ significantly lowers FID (indicating higher image fidelity) while simultancously enhancing scores related to text alignment and human preference (CLIP, ImageReward, PickScore, HPSv2), as highlighted by the best in orange and second-best in gray values. For instance, on Lumina-Next, FID drops from 26.93 to 22.49, and on Flux, FID improves substantially from 37.86 to 32.23, accompanied by consistent gains in human preference metrics. Furthermore, we evaluated performance on 72I-CompBend [14]. As shown in Table 2. Rectified- CFG++ consistently improves text-to-image model performance than does baseline CFG across all four attribute dimensions, indicating enhanced capability at generating images that accurately reflect complex compositional instructions. We provide more experimental results in Appendix D.3.
4.1.2 Intermediate Sampling Analysis
To understand the convergence dynamics and efficiency of Rectified-CFG++, we analyzed its gen- eration quality intermediate sampling steps. As may be observed in Fig. 3, standard CPG often introduces artifacts like oversaturation and high contrast early in the sampling process, and sometimes

---

APG
Flus
CFG-Zero
Rectified-CFGet
CRG
Guidance strategy comparison on SD3.5 [7].
Figure 5:
Figure T21 results from Flux [1] across pick-a-pic a-kk- pic [18] prompts.
SD3 [7]
SD335
Lumina [26]
CFG
Rectified- G++
CFG
Kectified- CFG++
CFG
Rectilied-CPGes
Prompt: deer made shinuerring starlight grazing beside silver rive...
Prompt: Ghost The Shell.
Prompt: A mermaid rocky shore, her tail shimmering with bioluminescent scoles
Prompt: crystal winged butterfly landing on a dewdrop-coveree spidenveb.
Prompt: Milky way lake.
Prompt: warrior princess brandishing ccrrrtal sword in a glowing battefield
Prompt: phoenix rising from garden fouantain, wings maid of blooming....
Prompl: Lyon Gallery ot Leica Store San Francisco.
Prompl: guardian golem curved from emerald stone standing vieil in oncient...
ART
ART LIVES
LO VESS
Prompt: grafiiti mural on a city wall saying 'ART LIVES' colorful...
Prompt: Newborn Baby Blanket Photography. Super Photo, Basket...
Prompt: A moonlit castle built atop wuterfall that glows with bioluminencent...
Figure 6: Comparison of CFG Rectified-CFG+ combined with SD3/3.5 [7] and Lumina [26] with diverse prompts. Rectified- CFG++ consistently better enhance semantic alignment, composi- tional balance, and generative fidelity across models and scenes.
significantly deviates from the target manifold. By contrast, Rectified-CFG+t maintains stable generation quality throughout the process. More detailed visualization examples are provided in Appendix D.
4.1.3 Qualitative Evaluation
Qualitative comparisons further illuminate the advantages of Rectified-CG++t Fig. 4 shows gener- ated text-to-image examples from the Flux [1] model combined with the default Conditional flow Standard CFG and Rectified-CFG++. Our method produced images having better semantic quality, alignment, details, and overall composition with less visible artifacts. Fig. 6 extends this

---

CFG
Rectifid-
CFG
Rectified-CFG+
CFG
Rectifted-CFC-
Cyber Curcrre Cafe
CyberCore Cafe
Prompt: sign saya
Prompt: airship soil mid-tear storm. Prompt: magical embedded stone.
CoberCCone Café", glowing in magenia and blue.
reveraling phruse WINDWRAITH CREST"
with the name 'SOLARFANG etched along its...
Fallro
ALL STOP MAY
STOP
Shrakpphy Delwarrd
ALL WAT
Prompt: A defective reading paper Hiled Feathered Conspiracies' headlnne in...
Prompt: stop sign below it
Prompt: mechanical butterfly landing scroll that reads 'Sitken Prophecy Delivered:'
Figure 7: Rectified-CFGrr enhances text generation quality. consistently improves the accuracy, legibility, and semantic alignment of text-to- rext-to-image models compared to standard CFG.
S03
503.5
lumina
Flx
8.E
62-
014
03
1943
12.00
307
19451
calor
19710
19110
02.5"
CTC 2one
AFG
CFC
Rociiied CTC
Figure 8: User study results comparing various guidance. The preference ratio indicates the percentage of participants that preferred images created using Bectified-CFG++ over those created using CFG terms of detail preservation, color consistency, and prompt alignment.
comparison across SD3 [7], SD3.5 [7], and Lumina [26] using diverse curated prompts. Again, Cectified-CGG++ consistently better enhanced semantic alignment, compositional balance, and overall generative fidelity across all models and prompt types. Fig. 5 visually compares different guidance methods. While standard CFG often suffers from oversaturation and misalignment, and other methods like APG [33] and CFG-Zero* [8] offer partial improvements but compromise on detail or geometric accuracy, Rectified-CFG+ reliably yields more faithful, high-quality output.
Text Legibility: Importantly, Rectified-CFG+ significantly improves the rendering of text intent within images, a known challenge of diffusion models. As illustrated in Fig. 7, prompts containing specific text like "CyberCore Café" or "Feathered Conspiracies" are rendered with much greater accuracy and legibility using Rectified-FGG+t. The textual intent clearer, better integrated into each scene, and more semantically correct. Additional examples demonstrating improved text rendering are provided Appendix D.4.
4.1.4 User Study
To further validate Rectified- Doctifid-CFG+++'s CFG++'s performance, we conducted user study. For given prompt and base model, participants were presented with four images generated using standard CFG [13], APG [33], CFG-Zero" [8], and Rectified-CFes
each set presented in randomized order. They were asked select the best image based on the following criteria: Image Detail, Color Naturalness and Consistency, and Prompt Aligument (including text legibility). Figure 8 displays the user preference ratios, indicating the preference of Rectified-CFG+4 over the other guidance methods. More detail in Appendix D.2.
4.2 Ablation Studies
Guidance Scale and Sampling Steps: We investigated the impact varying the guidance scales and the number of sampling steps (NFEs). Fig. 9(a) shows FID, CLIP, ImageReward and Aesthetic scores plotted against the guidance scale parameters, iec. X Rectified-CFG+t maintained high

---

Table 4: Computational cost comparison of standard CFG and Rectified-CFG++.
Table 5: Ablation study of Rectified-CFG++
components on MS-COCO 1K samples.
Resolution
Guidance
NFEs|
FL.PPs
Runtime (5)
Configuration
FID L
CLIP
HPSv2 1
Aesthetic 1
512x512
CFG
28
0.61x10
5.3148
Unconditional
91.1180
0.1439
0.1870
6.1049
Rect-CFG++
20
0.61x100
5.3506
Prodictor
73.6981
0.3410
0.2969
6.1064
1024x1024
CTG
28
2.1x109
16.2617 17,8804
Corrector
74.6545
0.3414
0.2975
6.1047
Rect-CFG++
20
2.1x10"
Rectifid-CCFG
6.1587
((a)) Effect of guidance scale (Alw).
((b)) Comparison across sampling steps (NFEs).
Figure 9: Ablation study across guidance scales and sampling steps. Assessed using FID(upper left), CLIP(upper right), ImageReward(lower left), and Aesthetic Scores (lower right) for both (a) and (b).
performance and stability across wide range of scales, whereas standard CFG [13] swiftly degraded. This indicates that CFG [13] pushes samples further off-manifold. Figure 9(b) illustrates performance relative to the number of sampling steps (NFEs). Rectified CFG++++ consistently outperforms standard CFG, achieving better scores even with significantly fewer steps. This reinforces the findings in Section 4. 1.1.2 and underscores the efficiency gains enabled by our method.
To isolate the contributions of the key components of Rectified-CFG++ we conducted ablation study on MS-COCO 1K using FID, CLIP, HPSv2, and Aesthetic Score as shown Table 5. The outcomes show that removing any of the studied components leads to degraded performance compared the complete Rectified-CFG- method. The configuration combining both the predictor and corrector steps achieved the best overall scores, validating the effectiveness of our integrated design.
Component Analysis:
Beyond generation quality, practical deployment requires computational efficiency. As demonstrated in intermediate sampling analysis (Section 4. 1.2) and ablation studies Rectified-CFG- achieves high-quality results using the same number or fewer sampling steps (NFEs) compared standard CFG. Table 4 provides direct comparison of text-to-image model performance using Rectified-CFG+ against standard CFG, where both models' were run for similar runtimes. Rectified-CFGi (85.82) on COCO-IK. We would also like to highlight that Rectified-CFG++ achieves much better FID at 5 NFEs, compared to 40 NFEs of standard CFG (see Appendix D.3). In this scenario, Rectified-CFG++ required fewer NFEs, which translates to lower computational cost, reducing both total FLOPs and inference runtime while giving much better generation quality. These efficiency gains make BectifiedCCGG-- more suitable for applications demanding faster generation operating under resource constraints.
Computational Efficiency:
achieved much better FID score (74.47) than standard CFG
Conclusion and Discussion
We introduced Rectified-CFG++ predictor predictor-corrector corrector guidance for text-to- sot-to--mmae generative models that first follows the conditional velocity, then applies weighted interpolation. When combined with leading flow-based foundation models, Rectified Bectified-FGG+ consistently improved performance against all quality measurements. Furthermore, Bectified-CFG++ demonstrated greater stability across varying guidance scales, mitigating artifact and quality degradation issues frequently encountered when using CFG. user study confirmed perceptual gains in detail, colour fidelity and text alignment when using Rectified-CFG-- Because Dectified-CFG++ is training- free and adds negligible compute,

---

it can serve as a drop-in upgrade of existing flow- fow-matching generators. Future work will explore extensions to video and 3-D diffusion, and integration with preference- reinforcement guidance models.
6 Acknowledgment
This work was supported by the National Science Foundation AI Institute for Foundations of Machine Learning (IFML) under Grant 2019844, and computing support on the Vista GPU Cluster through the Center for Generative AI (CGAI) and the Texas Advanced Computing Center (TACC).
7 Ethics Statement
Given the rapid progress of generative models, has become easier than ever to produce convinc- ing-butt but potentially misteaiing-Syythetiic content. Although such tools unlock new efficiencies and creative avenues, they also raise important ethical challenges. Readers interested in a deeper treatment of these issues are referred to the discussion in [31].
8 Broader Impact Statement
Social impact: Image generation based on flow base models potentially have both positive and negative social impact. This method provides handy tool to the general public for wide variety of image generation which can help visualize their artistic ideas. On the other hand, our work on improving improving sampling quality in these modes pose risk of generating arts that closely mimic or infringe upon existing copyrighted material, leading to legal and ethical issues. More broadly, our method inherits the risks from T2I models which are capable of generating fake contents that can be misused by malicious users.
This work builds upon the official implementations and pre-trained weights of the foundation models referenced in the main text. These methods along with diffusers library has mechanism to filter offensive image generations. Our method Rectified-CG++ inherits these safeguards.
Safeguards:
Reproducibility:
Apart from the pseudocode and implementation details provided in the paper, the source code available on the project page: https://rect-cfa www.p.gggttti....eeooo.g..o..g.p githu...h...... io/.
References
[1] Black Forest Labs. Flux. 26, 28, 29, 30, 34
2024. 2, 5, 6, 23,
[2] Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale gan training for high fidelity natural image synthesis. arXiv preprint 18Xiv:1809, 12t1:180991109 2018. 2
John C Butcher. Differential equations, numerical methods and algebraic analysis. B-Series: Algebraic Analysis of Numerical Methods, pages 1-37. Springer, 2021.
Ricky T. Chen, Yulia Rubanova, Jesse Bettencourt, and David K. Duvenaud. Neural ordinary differential equations. In Advances in Neural Information Processing Systems (NeurIPS), pages 6571-6583, 2018. 25
[5] Hyungjin Chung, Jeongsol Kim, Geon Yeong Park, Hyelin Nam, Jong Chul Ye. Cfg++: Manifold- constrained classifier free guidance for diffusion models. arXiv preprint arXiv:2406.08077 2024. 2, 2,3, 4,
6, 25
[6] Prafulla Dhariwal and Alex Nichol. Diffusion models beat gans on image synthesis. In Advances in Neural Information Processing Systems (NeurIPS), pages 8780-8794, 2021. 2, 25
[7] Patrick Esser, Sumith Kulal, Andreas Blattmann, Rahim Entezari, Jonas Müller, Harry Saini, Yam Levi, Dominik Lorenz, Axel Sauer, Frederic Boesel, et al. Scaling rectified flow transformers for high-resolution image synthesis. In Forty-first international conference machine learning, 2024. 2, 5, 6, 7, 8, 25, 26, 28, 29, 30, 31, 32, 33, 36, 37
[8] Weichen Fan. Amber Yijia Zheng, Raymond A Yeh, and Ziwei Liu. Cig-zero*: Improved classifier guidance for flow matching models. arXiv preprint X1v.2503.383886 2025, 4, 6, 8, 24, 25, 26
10

---

[9] Will Grathwohl, Ricky T. Q. Chen, Jesse Bettencourt, Ilya Sutskever, and David Duvenaud. Fijord: Free-form continuous dynamics for scalable reversible generative models. In International Conference on Learning Reprexentatios (ICLR), 2019. 2, 25
[10] Jack Hessel, Ari Holtzman, Maxwell Forbes, Ronan Le Bras, and Yejin Choi Clipscore: reference-free evaluation metric for image captioning. arXiv preprint arXiv:2104.087/1 18, 2021. 2,
[11] Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by two time-scale update rule converge to a local nash equilibrium. Advances in neural information processing systems, 30, 2017. 2,
[12] Jonathan Ho. Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural 2020. 2, 25
information processing systems,
[13] Jomathan Ho and Tim Salimans. Classifier-free diffusiin guidance. arXiv preprint arXiv:2207.125500 2022.
2, 3, 4, 6, 8, 9, 23, 25, 26, 30
[14] Kaiyi Huang, Chengqi Duan, Kaiyue Sun, Enze Xie, Zhenguo Li, and Xihui Liu. Tži-compbench++: An enhanced and comprehensive benchmark for compositional text-to-image generation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2025.
[15] Gabriel Ilharco, Mitchell Wortsman, Ross Wightman, Cade Gordon, Nicholas Carlini, Rohan Taori, Achal Dave, Vaishaal Shankar. Hongseok Namkoong, John Miller, et al. Openclip. If you use this software, please cite it as below, 7, 2021..1.2 2,6
[16] Tero Karras, Miika Aittala, Tuomas Kynkäänniemi, Jaakko Lehtinen, Timo Aila, and Samuli Laine. Guiding a difffusion model with a bad version of itself. Advances in Neural Information Processing Systems, 37:52996-53021, 2024. 25
[17] Durk P Kingma and Prafulla Dhariwal. Glow: Generative flow with invertible 1x1 convolutions. Advances in neural information processing systems, 31, 2018. 25
[18] Yuval Kirstain, Adam Polyak, Uriel Singer, Shahbuland Matiana. Joe Penna, and Omer Levy. Pick-a- pic: An open dataset of user preferences for text-to-image image generation. Advances Neural Informatinn Processing Systems, 36:36652 36663, 2023. 6, 26
[19] Tuomas Kynkäänniemi, Miik Aittll,, Tero Karras, Samuli Laine, Timo Aila, and Jaakko Lehtinen. Applying guidance in limited interval improves sample and distribution quality diffusion models. arXiv preprint arXiv:2404.07724 2024. 25
[20] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dollár, and C Lawrence Zitnick. Microsoft coca: Common objects in context. In Computer vision-ECCV 2014: 13th European conference, zurich, Switzerland, September 12, 2014, proceedings, part 13, pages 740-755. Springer, 2014. 2,26
[21] Yaron Lipman. Ricky T. Q. Chen, Heli Bam-Hamu, Maximilian Nickel, and Matthew Le. Flow matching for generative modeling. In The Eleventh International Conference on Learning Representations, 2023. 2,
3, 25
[22] Yiming Liu and Yaron Lipman. Rectified flow: A marginal preserving approach to optimal transport. In International Conference on Machine Learning (ICML), pages 21607-21631 PMLR, 2023, 2, 3, 25
[23] Cheng Lu, Yuhao Zhou, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu. Dpm-solver: A fast ode solver for diffusion prohabilistic model sampling in around 10 steps. Advances in Neural Information Processing Systems, 35:5775-577 5787, 2022. 3
[24] Artem Lukoianov, Haitz Sáez de Ocáriz Borde, Kristjan Greenewald, Vitor Guizilini, Timur Bagautdinov, Vincent Sitzmann, and Justin M Solomon. Score distillation via reparametrized ddim. Advances in Neural Information Processing Systems, 37:2601 1-26044, 2024. 2
[25] Alex Nichol, Prafulla Dhariwal, Aditya Ramesh, Pranav Shyam, Pamela Mishkin, Bob McGrew, 1lya Sutskever, and Mark Chen. Glide: Towards photorealistic image generation and editing with text-guided diffusion models. In International Conference on Machine Learning (ICML), pages 16784-16804, PMLR, 2022. 25
[26] Qi Qin, Le Zhuo, Yi Xin, Ruoyi Du, Zhen Li, Bin Fu, Yiting Lu, Jiakang Yuan, Xinyue Li, Dongyang Liu, et al. Lumina-ine image 2.0: A unified and efficient image generative framework. arXiv preprint arXiv:2503.21758 2025. 2. 5, 6, 7, 8, 25, 26, 28, 29, 35

---

[27] Alec Radford, Jong Wook Kim, Chris Hallacy. Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, al. Learning transferable visual models from natural language supervision. In International conference on machine learning, pages 8748-8763. PmLR,
2021. 2, 6
[28] Aditya Ramesh, Prafulla Dhariwal, Alex Nichol, Casey Chu, and Mark Chen. Hierarchical text-conditional image generation with clip latents. arXiv preprint 2rX4::2004.061 2022. 2
[29] Aditya Ramesh, Mikhail Pavlov, Gabriel Goh, Scott Gray, Chelsea Voss, Alec Radford, Mark Chen, and Ilya Sutskever. Zero-shot text-to- image generation. In International conference on machine learning. pages 3921-8831. Pmnr, 2021. 25
[30] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Bjöm Ommer. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 10684-10695, 2022. 2, 25
[31] Negar Rostamzadeh, Emily Denton, and Linda Petrini. Ethics and creativity in computer vision. arXiv preprint arXiv:21 12.03111,, 2021. 10, 29
[32] Seyedmorteza Sadat, Jakob Buhmann, Derek Bradley, Otmar Hilliges, and Romann M Weber. Cads: Unleashing the diversity of diffusion models through condition condition-annealed sampling. arXiv preprint arXiv:2310. 17347, 2023. 25
[33] Seyedmorteza Sadat, Otmar Hilliges, and Romann Weber. Eliminating oversaturation and artifacts of high guidance scales in diffusion models. In The Thirteenth International Conference on Learning Representations, 2024. 2, 3, 4. 6, 8, 25, 26
[34] Chitwan Saharia, William Chan, Saurabh Saxena, Lala Li, Jay Whang, Emily L Denton, Kamyar Ghasemipour, Raphael Gontijo Lopes, Burcu Karagol Ayan, Tim Salimans, et al. Photorealistic text-to- image diffusion models with deep language understanding. Advances in neural information processing systems, 35:36479-36494, 2022. 2, 25
[35] Christoph Schuhmann. LAION-Aestheties. http:://laim..aabllg/laaioo httpb/oog/aionn-asstteiccc.//// 2022. Accessed: 2023-11-10. 2,
[36] Jascha Sohl-Dickstein. Eric Weiss, Niru Maheswaranathan, and Surya Ganguli. Deep unsupervised learning using nonequilibrium thermodynamics. In International conference on machine learning, pages 2256-2265. pmlr, 2015.
[37] Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-hased generative modeling through stochastic differential equations. In International Conference on Learning Representations (ICLR), 2020. 2, 24
[38] Bram Wallace, Mcihua Dang, Rafacl Rafailov, Linqi Zhou, Aaron Lou, Senthil Purushwalkam, Stefano Ermon, Caiming Xiong, Shafiq Joty, and Nikhil Naik. Diffusion model alignment using direct preferenee optimization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8228-8238, 2024. 6
[39] Xi Wang, Nicolas Dufour, Nefeli Andreou, Marie-Paule Cani. Victoria Fernández Abrevaya, David Picard, and Vicky Kalogeiton. Analysis of classifier-free guidance weight schedulers. arXiv preprint arXiv:2404. 13040, 2024. 25
[40] Xiaoshi Wu, Yiming Hao, Keqiang Sun, Yixiong Chen, Feng 7hu, Rui Zhao, and Hongsheng Li. Human preference score v2: A solid henchmark for evaluating human preferences of text-to-image synthcsis. arXiv preprint 2306.23306.099
2023. 2,
[41] Mengfei Xia, Nan Xue, Yujun Shen, Ran Yi, Tieliang Gong, and Yong-Tin Liu. Rectified diffusion guidance for conditional generation. arXiv preprint 18777.7.77....77 2024. 4, 25
[42] Jiazheng Xu, Xiao Liu, Yuchen Wu, Yuxuan Tong, Qinkai Li, Ming Ding, Jie Tang, and Yuxiao Dong. Imagereward:
Learning and evaluating human preferences for text-to-image generation. Advances in Neural Information Processing Systems, 36: -5903-155593, 2023. 2, 6
[43] Candi Zheng and Yuan Lan. Characteristic guidance: Non-linear correction for diffusion model at large guidance scale. arXiv preprint arXiv:2312.07586 2023. 2.25
[44] Hongkai Zheng, Weili Nie, Arash Vahdat, Kamyar Azizzadenesheli, and Anima Anandkumar. Fast sampling of diffusion models via operator learning. In International conference on machine learning. pages 42402.
42402, PMLR, 2023, 2
12

---

NeurIPS Paper Checklist
The checklist is designed to encourage best practices for responsible machine learning research, addressing issues of reproducibility, transparency, research ethics, and societal impact. Do not remove the checklist: The papers not including the checklist will be desk rejected. The checklist should follow the references and follow the (optional) supplemental material. The checklist does NOT count towards the page limit.
Please read the checklist guidelines carefully for information on how to answer these questions. For each question in the checklist:
You should answer [Yes], [No], or [NA].
[NA] means either that the question is Not Applicable for that particular paper or the relevant information is Not Available.
Please provide short (1-2 sentence) justifiicton right after your answer (even for NA).
The checklist answers are an integral part of your paper submission. They are visible to the reviewers, area chairs, senior area chairs, and ethics reviewers. You will be asked to also include (after eventual revisions) with the final version of your paper, and its final version will be published with the paper.
The reviewers of your paper will be asked to use the checklist as one of the factors in their evaluation.
While "[Yes] " is generally preferable to "[No]", ", it is perfectly acceptable to answer "[No] provided proper justification is given (e.g., "error bars are not reported because it would be too computationally expensive" or "we were unable to find the license for the dataset we used"). In general, answering "[No] or "[NA] is not grounds for rejection. While the questions are phrased in binary way, we acknowledge that the true answer often more nuanced, so please just use your best judgment and write justification to elaborate. All supporting evidence can appear either in the main paper or the supplemental material, provided in appendix. If you answer [Yes] to a question, in the justification please point to the section(s) where related material for the question can be found.
IMPORTANT, please:
Delete this instruction block, but keep the section heading "NeurIPS paper checklist",
Keep the checklist subsection headings, questions/answers and guidelines below.
Do not modify the questions and only use the provided macros for your answers.
1. Claims
Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Question:
Answer: [Yes]
Justification: We have made main claims that accurately reflect the paper's contributions and scope in the abstract and the introduction.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or
NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
13

---

Justification:
The paper discusses the limitations of this work.
Guidelines:
The answer NA means that the paper has limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create separate "I "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model sellispecifiitiinn asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-texi system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and faimesss.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory Assumptions and Proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
Answer: [Yes]
Justification: We provide the full set of assumptions in Section and discuss the complete proof in detail in Appendix A.
Guidelines:
The answer NA means that the paper does not include theoretical results. All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced in the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should properly referenced.
4. Experimental Result Reproducibility
Does the paper fully disclose all the information needed to reproduce the main perimental results the paper to the extent that affects the main claims and/or conclusions of the paper (regardless whether the code and data are provided or not)?
Question:
Answer: [Yes]
Justification: The paper provides all the information needed to reproduce the main experi- mental results.
Guidelines:
14

---

The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way accomplish this, but reproducibility instructions for how to replicate the results, access to a hosted model (e.g.. in the case of large language model), releasing of a model checkpoint, other means that appropriate to the research performed.
also be provided via detailed
While NeurlPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) the contribution is primarily a new algorithm, the paper should make clear how to reproduce that algorithm. (b) If the contribution is primarily new model architecture, the paper should describe the architecture clearly and fully.
(c) If the contribution is a new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome deseribe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [Yes]
Justification: We have provide the core file of our code in the supplementary. And the code will be released upon acceptance.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips.. cc/
public/guides Sonidees/CoeSSumsssiiiiooo stibbmissssooocccyy for more details.
While we encourage the release of code and data, we understand that this might not be possible, "No" an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurlPS code and data submission guidelines (https: / mnips.cc/publitt wwwpc//gggeeeeeeeee (CodeSubmiiii aasionoPiccy) for more details.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
15

---

At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended to the paper) recommended, but including URLs to data and code is permitted.
6. Experimental Setting/Details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: The paper specify the all details of experiment, including hyper- parameters, the rationale for their selection and underlying model.
Guidelines:
The answer NA means that the paper does include experiments.
The experimental setting should be presented the core the paper to level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, supplemental material.
7. Experiment Statistical Significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [No]
Justification: We focused primarily on the exploratory analysis and preliminary results. Addressing statistical significance and error bars will priority in our future research to provide more comprehensive evaluation of our findings.
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi- dence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.
The factors of variability that the error bars capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall
run with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g., Normally distributed errors).
should be clear whether the error bar is the standard deviation the standard error of the mean.
is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates).
If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
8. Experiments Compute Resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
Question:
Answer: [Yes]
Justification: We provide implementation details including compute resource, time, etc.
16

---

Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper).
9. Code Of Ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurlPS Code of Ethics https: httppp////errsp...pppbiil//c///e peubllteEthccccuddeeneeesee csGuideliness ines?
Answer: [Yes]
Justification: The research conducted in the paper conform with the NeurIPS Code of Ethics in every respect.
Guidelines:
The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special cireumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g.. there a special consid- eration due to laws or regulations in their jurisdiction).
10. Broader Impacts
Question: Does the paper discuss both potential positive socictal impacts and negative societal impacts of the work performed?
Answer: [Yes]
Justification: Yes, we discuss the broader impacts in appendix section G.
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there are negative societal impacts, the authors could also discuss possible mitigation strategies (c.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility ML).
11. Safeguards
Question: Does the paper describe safeguards that have been put in place for responsible release of data models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
17

---

Answer: [Yes]
Justification:
Yes, we discuss it in section G in appendix.
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Question:
Answer: [Yes]
Justification: We follow the open- codebases throughout experiments, which credited properly.
Guidelines:
The answer NA means that the paper does not use existing assets.
The authors should cite the original paper that produced the code package or dataset.
The authors should state which version of the asset is used and, if possible, include URI
The name of the license (e.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.
assets are released, the license, copyright information, and terms use in the package should be provided. For popular datasets, paperswi wwwoee com con/datasete has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that are re-pane re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
If this information is available online, the authors encouraged to reach out the asset's 's creators.
13. New Assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [Yes]
Justification: We provide demo code in supplementary material. The complete source code will be released upon acceptance.
Guidelines:
The answer NA means that the paper does release assets.
Researchers should communicate the details the dataset/code/moodll as part their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset used.
At submission time, remember to anonymize your assets (if applicable). You can either create anonymized URL or include an anonymized zip file.
18

---

14. Crowdsourcing and Research with Human Subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given participants and screenshots, if applicable, as well as details about compensation (if any)?
Answer: [Yes]
Justification: We discuss the details of subjective study briefly main paper, and extensively in the appendix.
Guidelines:
The answer NA means that the paper does not involve crowdsoureing nor research with human subjects.
Including this information in the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included the main paper.
According to the NeurIPS Code of Ethics, workers involved data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
Answer: [Yes]
Justification: Yes, IRB approvals were obtained for the subjective study. All participants have provided informed consent. All personal information was properly anonymized.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Depending on the country in which research is conducted, IRB approval (or equivalent)
may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
19

---

Appendix
This supplementary material justifies the theoretical claims stated in the main paper, supporting the mathematical soundness and practical robustness of Bectified-FGG+ Here the outline of the supplementary material:
Proofs and Additional Derivations.
Pectified-CGG+ Interpretation.
Related Work.
Additional Experiments.
Failure Cases and Limitations.
Ethics Statement.
Broader Impact Statement.
Prompt List
A Proofs and Additional Derivations
A.1 Manifold Preserving Property of the Rectified-CFG+
Throughout, let Mr C Rd denote the (latent) data manifold time EE [0, and assume the network ty has been trained with the conditional flow-matching objective (Eq. (2)). Consequently, both the conditional and unconditional velocity fields tangent to Mr at every point:
Mr,
E T..Me.
(A.1)
[Tt: y)
U/ U Iz, t, Ø)
Recall the linear probability path Mr {(1 t)zo + tz ue (xre (r)) = Ø1 To be the target velocity. For any is E Mr there exists a latent pair (Zo, 2z such that 24 (1 t)z0 tæ
2o po. I1 ~N f)} and let
Lemma A.1 Manifold-Faithie Corrector) ). Let Mr. Perform Rectified- CFG step with step size At > O, with initial predictor update as - and corrector guidance as 0, giving the final update as #1-1=ODEUpdate(nn, t, 0e ). Assume || || I for E [t -
At t). Assume
2
the network is e-accurate, i.e. ||l| ur and ||1 u, |l s a for every E .t.. Then, for sufficiently small At
Mesi traiiinn croor namerical srmn
CE
At
(9)
Proof. On Mi-Ac- For the latent pair (Fo, 21) that generates T4, define:
ai = (1 (t At)) + - -t)) = It + At (u((
Since flows are tangent from 1, we have uf. o² E Tr, Mr: hence their linear combination é also lies in Tz_ A M, at. Therefore the corrector displacement is tangent to M, Rewriting the corrector guidance with true velocity
dr (vf uz) (1) oe -w) (()) -.).
The e-accuracy assumption implies ||ù; - u/| < (1 + 20max) E. Hence,
| ال-د At || well < (1 + 20 At.
(A.2)
Because at M,- the left-hand side of (A.2) is upper bound on dist (Fr, (I,- completing the proof.
Mi-ae)
20

---

A.2 Proof of Lemma 3.1
Lemma A.2 (Stability of Predicted Guidance Direction). Under assumptions (A1) and (A4), the guidance direction S computed the predicted state 11-21/2 differs from the guidance direction Ael (2x) at the current state by an amount proportional to the step size 2
| 0:/2 Ael S LV VV At.
(10)
Proof. Let 5 D1-2 + / By definition, Au 20/-11/2 (2 v" and A (x+) - v" (xt)) We want to bound
A A Augll:
| 21/2 Anl (1()(()) - - - (v](()) (x+))))
(1(v(()) of (v (f)
(Applying Triangle Inequality)
[lu{(()) uf (xx) |1""" (Ø) (x)i)
By assumption (AI), of and ex Lipschitz continuous with constant L:
- A - L|| - zell + -|l x
= 21. | =iell-
Substitute the definition of ::
| - æell = 11(0 + Atel/2) - mell = 11 21/21|/f11
By assumption (A4), ||u||| S Vmax. Therefore:
A Au 21/2 Ao!' S L(AtVmax) At
A.3 Proof of Proposition
Proposition 2 (Bounded Single-Step Perturbation). Let 3t-1 be the result of one Rectified- FaiiieeddCFG+++ +FG++ step from Fz- Let _t-1 I, At of (x,) be the result of pure conditional Euler step. Under assumption (A2), the deviation is:
(11)
Proof. Using the definition of Ehe from Eq. (8):
i = ODD.D Ft dxe)-
The pure conditional step is:
J,-1 2t Alv
Subtracting these two equations:
- 11-1-1111 = (xe + Atv. + Ata(t) - (x. + Atuf)
f1-1 -t-1 Av
Taking the norm:
|| - - ||| = (lt (t = (to Aw2ll-
By assumption (A2), the guidance direction magnitude is bounded by B. Hence,
|| -1-11l < Ata(t)B.
21

---

A.4 Bounded Distributional Deviation of the Rectified-CFG+
We now formally establish the bounded distributional deviation of CeetifiedCCG++* Proposition 3 (Bounded Distributional Deviation). Let pt denote the true conditional distribution evolving under the true velocity ut, and let Pt denote the generated distribution evolving under the model's effective velocity iz Their evolution governed by the continuity equation:
Öp: Ōt
+ V. (pru)) O.
(12)
The time evolution of their KI. divergence is given by:
dt DxL(fellp.) = Exup, (V (o - V (log (6((x) u (x))
(13)
Then, the final distributional error of Rectified-FFG+ is bounded as
DRL(Pellp.) & C. LV max At) / a(t)
(14)
where Csyy cv. B, L,, Vmax are finite constants.
Proof. Starting from the integrated KL evolution and applying the Cauchy-Schwarz inequality:
(RI(Felle)) s f Eampp. log - V log || - ue dr.
We separately bound the velocity error and score error:
Velocity error: For Rectified-CFG+
0g of + a(t) AU From Lemma 3.1 and the e-accuracy assumption, obtain
| u.l S 6 + aB)) + LVmax
Score error: The predictor-correcto mechanism (Lemma A.I) ensures the sampling process remains proximally close to the latent manifold, i.e. supp(p;) c To(My. Within this stable region, both V loog Pt and V log remain bounded, and their difference is upper bounded by finite constant C.,
Combining: Plugging these bounds into the KL derivative:
d DKL DKL(Pell) (Pelle)) s Ex-p/Cs + (B(((B + Wf)x)())].
dt
Integrating from t
0 yields the claimed final error bound, proving distributional stability.
This result strengthens our central claim: the manifold-constraint of Cecified-CFG-+ ensures stable, corrective evolution of the generated distribution.
B RectifiedCCG++ Interpretation
B.1 Geometric intuition
The overall Rectified-CFCt displacement is a linear combination of already-trusted directions ( conditional and unconditional ) Hence the trajectory is "projected" onto the local tangent plane at every step, preventing the dramatic colour saturation and structural distortions that may arise when
No orthogonal component of the form Ave with a new Av. & Mr is introduced, in contrast to standard CFG when
22

---

Figure 10: Samples produced by Flux-dev [l] using ReetifiedCFG+++
trajectories leave M, (Fig. 2). Rectified-CFGua sampling method can be viewed geometrically as manifold-conssraineed trajectory refinement approach.
RectifiedCCGG++ first performs conditional predictor step, projecting the latent state onto the learned manifold, then ensures that each intermediate representation remains manifold-aligned. Subsequently, the adaptive corrector step applies controlled. manifold-aware adjustment towards the conditional trajectory. Geometrically (see Fig. 1), this two-step process ensures that trajectories smoothly traverse along manifold, allowing precise guidance towards text-conditioned regions without manifold deviation overshoot. Consequently, our method achieves both precise generation aligned with the text conditions, and stable intermediate states that avoid drifting off aff-manifold (sce Fig. 3), significantly mitigating the artifacts typically induced by using CFG [13].
B.2 Enhanced Text Alignment and Manifold-Aware Generation
Rectified-CFG-4 sampling achieves significantly improved text alignment by adaptively correcting trajectories closer to the underlying learned data manifold. Traditional CFG approaches often push generated images away from the natural manifold due to aggressive conditional updates, causing unnatural distortions and poor aesthetics. Geometrically (see Fig. 1), this controlled navigation across the latent space prevents manifold deviation, preserving intrinsic visual coherence and semantic consistency. Consequently, our method delivers images that not only more precisely match textual descriptions but also exhibit significantly enhanced quality, characterized by reduced visual artifacts, greater perceptual realism, and smoother, more natural intermediate representations. Because the update never strays far from Mr, the model can faithfully realize additional conditional signals (text prompts) without wasting capacity "returning" to the manifold. Empirically, this yields better text-alignment and lower FID scores across guidance scales. Lemma A. explains that improvement direct consequence of geometric consistency.
23

---

1+18
1448 1408 1464 1407 1400
Figure 11: Following [8], we show comparison of sampling trajectories under CFG (top row) and Rectified-CFG+t (bottom row). Each column shows the evolution of 200 latent samples from 1.0
0.0 (left to right). Markers: the blue (top) and green (bottom) points trace the sample positions; the red star marks the target. Under standard CFG, the trajectories initially drift off the learned transport wanifold-pullinge sharply toward the conditional target only later steps-res resulinns in abrupt, off- manifold jumps. In contrast,
Mecifiid-CFG++ maintains a smooth, on-manifold path: the predictor step keeps samples close to the learned flow, and the corrector applies controlled interpolation that steadily guides them toward the target.
B.3 Remark on guidance weights.
Throughout this paper we have described Rectified-CFUS + combination of unconditional and conditional velocity fields with a time-dependent weight a(t) ( :_.:
, =f + a(t) - "
For many flow- cow-matching models (e.g. Flux) we obtain best results when 0 11, yielding true interpolation that keeps the trajectory fimmly on manifold. However,
CCttified-CF++++ is not restricted to a() S On models where the initial sampling steps are noticeably dependent on conditional branches, we deliberately allowed (<( > 1 during the early (high-noise) portion of the trajectory, then decay below as The same predictor/corrector structure still applies; the method merely chooses schedule that pass through both interpolation and mild extrapolation regimes while remaining numerically stable. We therefore treat (t) as a time-scheduled re-weighting rather than strict convex coefficient:
(tt)= = A (1- t)², Amax 2 0, >>
(15)
with Amax tuned on model basis. When Amax 1 the early steps behave like soft extrapolation, yet the empirical results $4 show that the rectified predictor-corrector architecture still prevents off-manifold divergences often observed when using naïve CFG.
Algorithm 2 RF sampling with CFG
Require: Trained Flux model vp, condition time steps N, step size At 1/N,
1: (2(
> Sample from noise distribution
2: for 0, 1, ......N do
3:
t, = nAt
4: 0g (1 w) wof
5:
Ita-1 Ft.. + At 0g
> ODE
6: end for
7: return 20
C Related Work
C.1 Diffusion Models
Diffusion models (DMs) learn a stochastic (or deterministic) reverse process that gradually converts Gaussian noise into natural images. Pioneering score-based work [37] and the DDPM formulation

---

Table 6: Sampling update rules for various guidance strategies. All methods operate in latent flow space using a velocity function (2 t,.). Sectified-CGG+e introduces a predictor-corrector formulation combining unconditional drift and conditional correction.
Method
Velocity Functions Used
Update Equation
CPG
(o( 1,
At w) oa(2e, f. (x
APG
t,) Auf
At [oo t, + Aufu.r.8))
CFG-7em*
Mo(2, na(z,
At
w) of oo(2e, + (
Ceet-CFG++ooet,t// vals, c) E1+1
Py(=ns fu. + a(t.) ) (vo(=,. 4. v) vals An 01)
of [12] established the foundations that later enabled large-scale text-to-image systems such as GLIDE [25], DALLE [29], Imagen [34], and Stable Diffusion [30, 7]. Architectural innovations-c.2
latent-space diffusion [30] improved sample quality and inference speed.
C.2 Flow based Generative Models
Normalizing flows (NFs) parameterize invertible transformation with a tractable Jacobian determi- nant. Early discrete NFs (e.g. Glow [17]) were eclipsed by Continuous Normalizing Flows (CNFs) that solve ODE defined by a neural velocity field [4, 9]. Recent flow Now-matching objectives cast generative modeling as learning a vector field that transports noise to data along a predefined sched- ule [21]. Rectified Flow (RF) [22] shows that simple mean-squared objective suffices, eliminating simulation noise and yielding fast ODE solvers. In the text-to-image domain, model like SD3 [7], Lumina-Next [26]. and FLUX [1] combine RF objective with large multi-modal diffusion transformer deliver competitive image quality.
C.3 Guidance in Diffusion Models
Classifier guidance (CG) [6] injects gradients from external classifier but demands high-accuracy auxiliary network. Classifier- Free Guidance (CFG) [13] sidesteps this re- quirement by training conditional and uncon- ditional networks jointly and linearly extrapolat- ing their predictions during sampling. While CFG is now ubiquitous [25, 34, 29, 7], the high guidance scale pushes samples off the data manifold, causing over-saturation and structural collapse [5, 33]. Recent work re- places the single extrapolation with adaptive weighting or updates in sampler: Dynamic thresholding [34], CADS [32], ReCFG [41], characteristic- guidance [43], weight sched- ulers [39], Interval guidance [19]. CFG++ [5], APG [33], AutoG [16], and step-limited CFG [19]. All are designed for stochastic dif- fusions; they either cannot be translated to flow
Ractfled-CFG++
based models, or underperform or destabilize the ODE trajectory [8].
Figure 12: Comparison of T2I results using Flux, with CFG, and with Rectified-CFG++
CFG accumulates error over sampling steps, that scales with the norm of the unconditional velocity. These observations motivate our design of RectifiedCCGG+t we reinterpret guidance as an interpolation in velocity-field space and embed coriicor-corrector it in an FM-compatible predictor corrector ODE solver. By anchoring each predictor step with conditional update to anchor the trajectory along the learned transport path and scheduling a purely interpolative corrector, we preserve the manifold geometry learned by the flow while still reaping the alignment gains of strong guidance. Extensive experiments show consistent improvements over vanilla CFG and its DM-centrie variants across all flow based models.
25

---

D Additional Experiments
D.1 Implementation Details
All experiments were conducted on single NVIDIA A100 40 GB GPU. Code was written in Python 3.10, using Py PyTorch 2.0.1 and the latest HuggingFace Diffusers library. We evaluate four flow-based text-to-image backbones, taken from huggingface diffusers:
Stable Diffusion 3 [7] (SD3) and 3.5 [7] (SD3.5): public weights from
and -aabllittaal//ttaleedddfuuiiisi 3.5--arge.
Flux-dev [1]: guidance-distilled Flux models from black-forret-Dabs//UUX 1-dev.
Lumina [26]: public weights from BaaaaaaWWLW//mmmaa-mmageeee
All models generate 1024 1024 images from text prompts without additional fine-tuning.
D.2 Details of User Study
To assess perceptual quality and prompt fidelity, we conducted blind four-way forced-choice comparison subjective study. No personally identifiable information was collected and standard guidelines for interacting with human subjects were followed. There risk incurred and no vulnerable population.
Participants & Prompts: We recruited 30 unique expert workers with knowledge of image processing, generative AI, computer vision, etc. Each worker was shown 32 distinct text prompts (e.g. "a number people standing around a large group luggage bags"), randomly sampled from our MS-COCO 10K [20] subset and Pick-a-Pic 1K [18].
Interface & Instructions: For each prompt, participants saw four generated images from particu- lar T2I model one per method (CFG [13]. APG [33], CFG-Zero* [8], and Dectiied-CFG+H1 in randomized order. The survey page (Fig. 13) instructed them to select the best image on four factors:
Detail: fine structures and textures.
Naturalness & Color: realism of scene and color consistency.
Text Legibility: clarity of any embedded text or signage.
Overall: overall holistic preference.
Participants encouraged to switch to larger screen zoom if necessary to inspect fine details. We repeated this for all four T21 models, i.e. SD3/3.5 [7], Lumina 2.0 [26], and Flux [1].
Data Collection: Each (prompt, generations) pair was rated by 30 independent expert participants, yielding 15360 total responses across all four T2I models. Image positions and prompt order were fully randomized mitigate presentation bias.
We aggregate per-pair preferences for each method, the fraction of times was chosen as best. As shown in Fig. 8, Rectified-CFG++ is preferred over all alternatives on Detail, Naturalness & Color, Text Legibility, and Overall confirming its advantages in fine detail, color fidelity, and prompt adherence.
D.3 More Quantitative Results
Here, we report further metric-based comparisons of Rectified-CFCC across multiple datasets, models, guidance scales, and sampling budgets.
LAION-Aesthetio and Pick-a-Pic Evaluations: Table summarizes performance on the LAION- Aesthetic IK subset. Rectified-CFG++ consistently lowers FID and improves Ccore,, ImageRe- ward, PickScore and HPSv2 across all four backbones. For example, on Flux-dev the FID drops from 120.13 13 to 112.19, while ImageReward jumps from 0.0968 to 0.6849, Table 8 presents results
26

---

Welcome! Thank you for your help in improving the next generation of text-to-image models.
You will see now 32 sets of images in total. Please select your preference for the best image out of the displayed images.
Overall, you may consider the following factors: image detail, realism of scene, color naturalness and consistency, prompt alignment, and text fidelity. Pay special attention to artifacts like malformed hands or limbs, misshaped objects, and so on.
Please switch to a larger pereen/zoom to observe details if you find providing ratings difficult.
sooue the boach stoees
Detall
Naturainess and color:
Text legibility:
Overal::
Please select image disployed on following factors. The corresponding lobels are balow each Image. fastor is nor applicabll please leave blank.
Figure 13: Interface for the study. Top: participants first read detailed instructions the evaluation criteria (detail, naturalness & color, text legibility, overall) and usage guidelines (e.g. zooming, screen size). Bottom left: an example text prompt together with the four generated images shown in randomized order. Bottom right: the corresponding multiple-choice rating options for each criterion, where workers select which of the four images best satisfies the given factor.
27

---

on the Pick-a-Pic IK prompts. Rectified-FG++ yields uniformly higher CLIP-Score, Aesthetic, ImageReward, PickScore and HPSv2.
Guidance Scale Ablations: Table reports FID, CLIP and ImageReward for Flux-dev [1] under six different guidance scales (w, A). Across all settings frrtings-from mild to aggressive Buidance-Rectifeer CFG++ matches or exceeds CFG, with best results highlighted in orange. Table 10 extends this multi-scale comparison SD3 [7] and SD3.5 [7] on both MS-COCO-IK and LAION-Acsthetic
Sampling Step Ablations: Finally, Tables 11, 12 and 13 compare standard CFG and Rectified- CFG++ the number of function evaluations (NFEs) varies from 5 to 60. Even with few NFEs, Rectified-CFCC
reduces Flux [1]'s FID from 177.8 to 71.2 and boosts ImageReward by over 2.4 points. Similar gains are observed SD3 [7] and SD3.5 [7]: at 15 NFEs, SD3's FID falls from 72.7 to 69.1, and at 28 NFEs SD3.5's ImageReward rises from 0.72 to 0.77. These results confirm that Rectified-FG++ limited sampling budgets.
only improves ultimate quality but also accelerates convergence under
D.4 More Qualitative Results
To complement our quantitative evaluation, we present extensive qualitative evaluations across four state-of-the-ar flow-based text-to-image backbones (SD3 [7], SD3.5 [7], Flux-dev [1], and Lumina 2.0 [26]). each case we select diverse, challenging prompts ranging from signage and typography to fantasy scenes, and text-heavy compositions and show side-by-side renderings in Figures 14-18. 18.
Improved Prompt Fidelity and Detail: Across all models, Rectified-CFG+ better captures the precise wording, style, and layout of complex text prompts. In Figure 14 (top) the "Welcome to Dustvale" billboard exhibits crisp, correctly proportioned lettering under Rectified-CFOO CFG++ whereas CFG renders unclear and distant characters. Similarly, for the "Elixir of Time" grimoire (Figure 14), our method preserves fine runic serifs and balanced illumination, avoiding the blotchy over-saturation and gibberish text seen with CFG.
Enhanced Geometry and Color Balance: Rectifie--FFG+ produces more coherent object shapes and natural color distributions. In the ruined observatory prompt (Figure 14, middle left), the dome geometry remains intact and the night-sky hues appear smoothly graded, in contrast the heavy color clipping and warped glass panes under CFG.
Robustness Artistic and Text-Intensive Tasks: In text-heavy or highly stylized contexts (Figures 19-20), CFG often fails to form legible letters or distorts ornamented scripts, whereas ReetifiedCFG+++ maintains semantic clarity and faithful adherence to prompt instructions. For example, the medieval scroll ("Quest Accepted") and the glowing "IGNIS SCRIPTUM" spell circle rendered with sharp, even strokes only under our method.
Stable Intermediate Trajectories: Figure 21 visualizes successive denoised latents for two prompts using both CFG and Dectified-CFG++ While CFG trajectories diverge off-manifold yielding over- saturated patches and incoherent forms in early timesteps, Rectified-CFGa remains tightly clustered, preserving anatomical and geometric consistency every step. Even with only 7 NFEs (Figure 22), our sampler produces high-fidelity results far sooner, demonstrating accelerated convergence.
Generalization Across Models: Figures 16, 17 and 18 confirm that these qualitative gains extend across all flow-based models tested- SD3 [7]. SD3.5 [7]. Flux-dev [i], and Lumina 2.0 [26]. Whether generating playful scenes ("a cat in space suit skiing"), hyper-realistic product shots ("leaf-covered Porsche"), or fantastical landscapes (floating island cities, glowing jellyfish cathedrals), Rectified- CFG++ consistently yields crisper details, fewer artifacts, and stronger alignment to both text and style cues.
Together, these qualitative examples illustrate that the manifold-aware update of Rectified-CFG+ not only improves objective metrics but also delivers visibly superior images in a wide variety of challenging text-to-image scenarios.
28

---

E
Failure Cases and Limitations
Although Rectified-CFOG greatly reduces off-manifold artifacts, observe that, for prompts requiring multiple interacting objects the method sometimes misplaces secondary elements or fails to respect relative scale. On further investigation, we observe that these limitations arise from underlying T2I model, and is consistent across all guidance methods. Our approach, being entirely training- -free, inherits the dependence on pretrained velocity accuracy, any systematic bias normal-space drift in may propagate through Rectified-CGG++
F Ethics Statement
Given the rapid progress of generative models, has become easier than ever to produce convinc- ing ing-but potentially misleading -yynthetic content. Although such tools unlock new efficiencies and creative avenues, they also raise important ethical challenges. Readers interested in a deeper treatment of these issues referred to the discussion in [31].
G Broader Impact Statement
Social impact: Image generation with flow-based models potentially has both positive and negative social impact. This method provides handy tool to the general public for generating wide variety of images which can help visualize their artistic ideas. On the other hand, our work on improving sampling quality in these models poses risk of generating art that closely mimics or infringes upon existing copyrighted material, leading to legal and ethical issues. More broadly, our method inherits the risks from T2I models which are capable of generating fake content that can be misused by malicious users.
This work builds upon the official implementations and pre-trained weights of the foundation models referenced in the main text. These methods along with the diffusers library has mechanism filter offensive image generations. Our method Rectified-CFGi inherits these safeguards.
Safeguards:
Apart from the pseudocode and implementation details provided in the paper, the source code available on the project page: https://recttffed-ccffpp gittipp.ittubioo.
Reproducibility:
Table 7: Quantitative evaluation of Reetified-CFG+ across T2I models LAION-Aesthetie 1K samples. Best values highlighted orange, second-best in gray,
Model
Guidance
FID
CLIP t
Aesthetic
ImageReward f
PickScore
HPSv2
CBG
112.3344
0.2717
5.6823
0.4173
0.5913
0.2324
Lumina [26]
Recl. CFG++ (Ours)
110.4973
0.2771
5.6823
0.4108
0.4087
0.2098
CPG
107.2530
0.3092
6.0328
0,5800
0.4708
0.2464
SD3 [7]
Reci. CFG++ (Ours)
105.9037
0.3125
5,9750
0.6840
0.5292
0.2549
CFG
108.4551
0.3162
6.1245
0.6984
0.4798
0.2543
SD3.5 (7]
Rect. CFG++ (Ours)
107.3915
0.3164
5.9528
0.7635
0.5202
0.2569
CFG
120.1258
0.2939
4,8033
0.0968
0.3469
0.2181
Flux-dev [1]
Rect. CFG++ (Ours)
112.1902
0.3065
5.5694
0.6849
0.6531
0.2518
29

---

Table 8: Quantitative Evaluation of Rectified-FGG+ Across T21 Models on Pick-a-Pic 1K
samples. Best values highlighted in orange, second-best in gray.
Model
Guidance
CLIP f
Aesthetic
ImageReward
PickScore t
HPSv2 f
CFG
0.3336
5.6996
1.0080
0.5841
0.2910
Lumina [26]
Reet. CFG++ (Ours)
0.3378
5.8770
0.7621
0.4159
0,2982
CTG
0.3453
5,7286
0.8268
0.4908
0.2859
SD3
Rect. CFG++ (Ours)
0.3487
5.6441
0.9364
0.5092
0.2933
CFG
0.3551
6.0411
1.0181
0.5211
0.2980
SD3.5 [7]
Rect. CFG++ (Ours)
0.3564
6.8767
1.0267
0.4789
0.2996
CFG
0.3312
5.1419
0.5336
0.3428
0.2609
Flux-dev [1]
Rect. CFG++ (Ours)
0.3406
5.8455
0.9641
0.6572
0.2974
Table 9: Multi-scale quantitative evaluation of the Flux [1] model (28 NFEs) on MS-COCO
IK and LAION-A 1K. We implemented Flux [1] using both standard CFG [13] and Rectified-CFG++ CFG++ as the guidance scales (w, A) were varied. Lower (4) FID and higher (t) CLIP and
ImageRewarr scores indicate better performance. Best values highlighted in orange, second-best in gray, (Best viewed zoomed in.)
Methl
MIGCOCO 18
Bee-CPGes 16304
8346
14666
6.489
1,009
766191
63886
18388
8388
1827
754866
8363
14311
8363
LARON Amiheirs
054415
8303
61644
0J85
6781
48330
1981
6320
8393
619
66380 AJI0 6335
Table 10: Multi-scale quantitative evaluation of the SD3 [7] and SD3.5 (7) T21 models using CFG and Rectifed-CFG++ (28 NFEs) on the MS-COCO 1K and LAION-Aesthetie 1K datasets, as the guidance scales (w, A) were varied. Lower FID and higher CLIP ImageReward indicate better performance. (Best viewed zoomed in.)
Gabba
201 50
20)
FIBI
Ingleed
Deafledl
(3.0P)
TngRnd)
CLIP IegReed
3.34%
0.6177
01.31:21
6C7941
$.991
$2.800
09 08.15
8.405
1880
05322
K756
45.0544
6.00
18000
6.580
1C128
03485
1.8.00
(8.991
01.113
11882
S6392
LADON
37125
125,1900
113.230
1.675
03537
185439
6301
0686
001165
03183
37555
20 801
0107
121-081
2132
0620
111.34
0390
3.503
Table 11: Evaluation of the Flux [1] model across different sampling steps (NFEs) on MS-COCO 1K. We compare standard CFG and Rectified CFG++ across key metrics. Lower FID and higher
CLIP/mmageReward indicate better performance.
Steps
FID
CLIP
ImageReward
CFG
Recl.CCF++
CFG
Recl.CFG+
CFG
RecL-CFF++
.1.4
15
114
74.47
0.30
0.34
-0.38
1.04
75.34
0.32
0.34
0.46
78.47
74.13
0.34
0.35
0.80
1.04
50
76.88
75.17
0.34
0.35
0.92
1.01
60
85.82
75.34
0.32
0.34
0.47
1.02
Table 12: Evaluation of the SD3 [7] model across different sampling steps (NFEs) on MS-COCO 1K. Comparison between standard CFG and Rectified- -FG+f
Steps
CLIP 1
ImageReward f
CFG
Reci. CFG++
CFG
Rect. CFG++
CFG
Rect. CFG++
5
129.0333
112,8318
0.2654
0.2779
.I .1.4232
-1.08033
72.7270
69.0608
0.3418
0.6826
0.7326
28
72.7399
70.0272
0.3461
0.3432
0.8961
0.8294
40
72.8198
68.7318
0.3449
0.3453
0.9244
0.8836
50
73.4710
70.1959
0.3456
0.3463
0.9244
0.8710
60
73.2599
68.9540
0,3450
0.3456
0,9143
0.8986
30

---

Table 13: Evaluation of the SD3.5 [7] model across different sampling steps (NFEs) on MS-
COCO 1K. Comparison between standard CFG and Pectified-CFG++
ImageReward
Steps
CFG
Rect. CFG++
CFG
Rect. CFG++
CFG
Reci. CFG++
5
85.9537
149.3422 099.4422
0.3214
0.2300
-0. 0.1880
-1,5413
15
.994
69.3713
0.3430
0.6820
28
69,8250
69.1095
0.3435
0.3443
0.7274
0,7750
40
69 29929999
69.2601
0.3431
0.3437
0,7310
0.7708
69.36 69,3650
69.0434
0,3452
0.3443
0.7506
0.7705
60
68.8897
67,9782
0.3438
0,3441
0.7348
0.7611
CFG
Rectified-CFGe
CFG
Rectifed C+++
Weeeee to Distyval
Prompt: billboard on a desent highwayy showing 'Welcoe Dustvale' : retro 70s font, sun flore.
Prompt: magic tome opened to page glowing text that reads "Elixir of Time' in enchanted rines.
CFG Rectifled-CFGrt
CFG
Rectifedd C+++
STTONOVA
ASTIRONNDVA
Prompt: A rained celestial observatory at the edge of the world, its cracked glass dome revelinng rotating sky-map... Rectified C++++
Prompt: sct-it poster with tile ASTRONOVA
PRIME metallic lettering and lens flrrs.
CFG
CPG
Rectifed-CFG++
Prompt: fairy marketplace hidden inside giant blooming Blower stals glowing with enchanted trinkets, fruit that... Rectified CFFt
Prompt: A painting of desert nomad holding a glowing hourglass, time swirls around their rober. CFG
CFG
Prompt: colosial bioluminescent jellyfish cathedraf towering the deep with massive glowing coral...
Prompt: At the center of glowing sakura forest drenched in moonlight, mystical fox-like humanoid with radiant orange...
Figure 14: Outcome of the SD3 [7] T21 models when using CFG vs Ceetifiid-CFG-re for variety of prompts. Our method consistently improves image generation quality by producing more coherent, semantically aligned, and visually rich results, under complex or artistic prompting scenarios.
31

---

CFG
Rectified-CFCC
CPG
Rectified-CFG
Prompt: HID Wallpaper
Prompt: SpaceX ready to send first all civilian crew on... CFG
CFG
Rectiffed-CFG++
Rectifed-CCGG.
Prompt: Viiled Winion
Prompt: The One And Only by Tim Wolker Vogue May..
CFG
Rectified-CFGG:
(PFG)
Rectifed- CFG+
Prompt: Waterfall surrounded by nice early summer flowers. Heather Foothills, Mt. Hood Meadows Oregon... Rectified-CFGs
Prompt: Halloweer scores up 918 mu global box office second highest horror opening of North...
CFG
CFG Rectifed-CFGG.
Prompt: Stevens
Prompt: Man stands near waterfall CFG
CFG
Rectified-CFG-
Rectifed-CFGet
Prompt: At the glowing sakara forest drencked moonlight, a nyyatical fou-like hamanoid with radiant orange fur
Prompt: mujestic phoenix shimmering crystal flowing nebulue, soaring midair in a twilight sky filled with violet auroras...
Figure 15: Outcome of [7) when using CFG vs Rectified-CGG-r for variety text prompts.
32

---

Rectified CFG+
Rectified-
Prompt: An enchanted convon with footiigg stones engraved prophecy, golden birds nesting carved....
Prompt: A snowy village where aurora bovealis is woven into tapestries mythical weavers
Rectified
Prompt: A firefly festival deep bamboo forest, with Bloating lanteras spirit masks glewing nwilight. Rectified-
Prompp:: An underwater palace li by jeilyfish lantems, where merfoll armate hold Reclified-CPP
Prompt: glowing portal in the center of an anciens onk tree, guarded by moss-caveted sooe nwilight. Rectified-CFGe
Prompt: A sky harbor where airships duek on floaingg islands mode crystal, waterfials cascading
Rectified-FFCo
Prompt: A celestral stog made of Highting and auroras galloping across stormy sky, leaving trails of stardust its wake.
Prompt: flooting mountaann temple where monks ride beams of light meditate among the stars, surrounded by glowing ionus clouds.
Figure 16: More examples for SD3.5 [7] with CFG vs Rectified-CFG+r for a variety of text prompts.
33

---

Rectified-FGG+
Rectifled-CGG-
Prompt: cal in space sult skiing ReetifeedCFGG+
Prompt: A dos jumping in front of moon gate, purple... CFG
CPG
CFriieedd-FG+++
Prompt: smoll with face the sabara... CFG
Prompt: Porsche 911 covered with leaves showsoo..
Rectified-
CFG
Sectilee-CFGrr
Prompt: A super cute Pikachu Reetifeed-FGG+
Prompt: man deadlifting heavy we weighrs CFG
CFG
Sectihed-CFGee
Prompt: the rock dwayne johuson doing ballet.
Prompt: Photorealistic fossilised bronce sculpture
Figure 17: Outcome of Flux [1] with CFG Rectified-FG++ for variety of text prompts.
34

---

CFG
Rectified-CFF CFG++
CFG
Rectified CFG++
Prompt: A flnating island above of clouds with waterfalls cascading into the mist Rectified-CFGe
Prompt: twilight marketplace staffed by gobins solling
glowing gemstones.
CFG
CFG
RectifiedCCFGe
Prompt: treebridge sposning two mountain peaks under the aurona boraalis Rectified-CFGG
Prompt: of lavender with lotus flowers drifting
toword distant spired city,
CFG
CFG Rectified-CFG-
S
Prompt: A neon lt dragonfly queen presiding
Prompt: crystal dragon coiled oround ancient
CFG phosphorescent swamp.
under tapestry of stars.
Reclffed-CFG++
CFG Reclined-CFGs*
Prompt: marble satue goddets that dawnn's 's first light.
Prompt: hidden waterfoll that pours rainbow crystal pool below.
Figure 18: Outcome of Lumina [26] with CFG vs Rectifie-CFG++ for a variety of text prompts. Rectified-CFG- improves compositional clarity, color balance, and prompt adherence under fantas- tical and artistic conditions.
35

---

CFG
Rectifled-CFGa
Q
une arre this ane cu neceten dhemnem
For Uomtue anced on Cucepte ted Queey thest
Quest
Acepted
qoucre afeeraind maate
A Accepetted linn GHITE CAIRE CUIEE
Prompt: medieval scroll displaying phruse "Quest Accepted" in ornate gothic script.
CFG
Rectiffed-CFG+
EETRON ENNTETY
DOMNHON AOI ETENAL
NETRNAL
Prompt: A gianz, ancient coin partially baried in sow, engraved with 'DOMINION ETERNAL around its rim.
CFG
Rectifed-CFF++
NIGHTALL
Prompt: magical contract flouting miduir, the
glowing script.
Figure 19: Comparison of text generation using CFG against Rectified-CFG+ in the SD3.5 [7] (Part 1). Rectified-CFG++ improves legibility and semantic preservation, especially in stylized or aged contexts.
36

---

CFG
Recttfled-CFGHt
IGNIS SCRIPTUM
Prompt: golden speltcirele inseribed with the phrase 'IGNIS SCRIPTUM" in liquid gold rumes, hovering midait. Rectifee-CFG++
CFG
Breathe, Don't Bite.
Prompt: A licard monk painting 'Breathe Don't 't Bite" in perfect cursive rice poper with a brush
CFG
Rectified-CFG++
Entay amd the Souil
Entropy and the Soul
T
Prompt: fax giving TED ritted 'Entropy and Soul" digiual behind.
Figure 20: Comparison of text generation using CFG against Dectified-CFG+t in the SD3 [7] (Part 2). Even in highly decorative or weathered lettering styles, Rectified-CFG+t retains better visual clarity and accurate text composition.
37

---

Prompt: glamorous womun smiling glowing background
CPG
Rectifie- CRG++
Prompt: A Ayper-detalle dragon glowing orange iris, reptilian skin
CFG
Reetified CFC+++
Figure 21: Intermediate timestep visualizations of CFG and Rectified-CGG++ Progressive decoding of denoised latents across intermediate timesteps using CFG (top row) and RectifiedCCGG+ (bottom row). For each prompt, we used total of 14 sampling steps, progressing from 1000 (top left) to
(bottom right). While CFG suffers from unstable off-manifold transitions early resulting in oversaturated colors and incoherent forms, Rectified-CrG++ maintained consistent, semantically grounded updates throughout. This enables significantly improved anatomical realism, color harmony, and overall fidelity under reduced lesser computational budget.
38

---

Prompt: highly detailed sculpture of a dog entirely reflective gold, jump, fuuld metallic dynamic lighting.
CFG
Reetifed-CFFG C++
Prompt: celestial lion composed of stardust and transtucent supphire, resting atop a glowing moonrock pedestal under a swirling galary sky..
CFG
Rectifed-CFFG+
Prompt: At the center of glowing sakura forest drenched in moonlighs, a mystical fox like hamamoid with radiant orange for and nine
shimmering taifs stands guarding...
CRG
Rectifed- CFG+++
Prompt: Inside rained cotheddal overtakon by vines and time, mechanical ortisan half human, holf-clockwork adjucts flooting, glowing time orb...
CRG
Reethhed-CFC++
Figure 22: 7-step sampling comparison between CFG and RectifiedCFG++. Each pair of
rows shows intermediate denoised and decoded latents for all 7 sampling steps. Rectified-CFCC + consistently delivered better generated outcomes even in the early time steps while keeping the overall generation process on-manifold.
39

---

Table 14: Comprehensive list of prompts used across figures, experiments, and qualitative evaluations in the paper.
Prompt
mujestic phoenix made of shimmering crystul and flowing nebulae, souring miduir willight sky filled with violet auroras and floating petals. celestial fiom with translucent sapphire mane leaps thrugh swirling galaxy clouds under violet night sky, glowing stars trailing its paws. A lone unthupormorphic fox in crystulline samurai amnor, standing still in bamboo grove made of glass, glowing runes etched into each plate.
feathers dripping golden light, oil painting style. A mystical fox-like humanoid with nine shimmering tails, guarding floating paper lantern in glowing sakum forest. balf-buman, balf-clockwork artisan adjusting a glowing time orb inside a cathedral overgrown with vincs.
mujestic griffin stunding atop wind blown cliff at twilight, wings unfurled
5
made entirely of seflective molten gold, mid-jump, Buid metallic texture, studio lighting. sci fi poster with the bold tille ASTRONOVA PRIME' in metallic lettering and lens flures. hillhoard desert highway showing 'Welcome to Dustvale', retro 70s font, flare.
sculpture of
10
A fairy murkeiplace hidden inside giant blooming flower, stalls glowing with enchunted trinkets, fruit that flsuts midair. rained celestial observatory at the edge
world, cracked dome revealing rotating sky-mag of shifting stars.
12
A hyper-detailed dragon eye, glowing orange iris, reptilian skin.
13
glamorous woman smiling in glowing cosmic background.
14
golden spellcircle inseribed with the phruse IINNSS SCRIPTUM" liquid fire-gold runes, hovering middair. A mussive sand carved monument showing 'CITY OF WHISPERS' in eroded stone calligraphy.
15
16
magical contract floating in midair, the clause 'SOULBOUU BOUND BY NIGHTFALL glowing in arcane script.
17
A medieval scroll displaying the phrase "Quest Accepted" in ornate gothic script
giant, ancient coin partially baried snow, engraved with 'DOMINION ETERNAL: around its
19
A lizard monk painting Breathe. Don't Bite' in perfect cursive on rice paper with brush.
20
A fox giving a TED talk titled 'Entropy and the Soul' written on a digital board behind. in space suit skiing.
22
A small cactus with happy face in the Sahara desert.
dog jumping in front of moon gate, purple flowers, snowy mountains. A Porsche 911 covered with leaves in showmom.
24
super cute Pikachu.
26
man deadlitting beavy weights. The rock Dwayne Johnson doing bullet.
27
28
Photorealistic fossilised bronze sculpture face portmait.
29
A magical deer made of stars standing at the edge of glowing river under an aurora.
knight made of stepping through shattered stained-glass portal.
31
A cloaked traveler entering glowing cavern of crystal pillars.
32
mysterious violinist in a foggy alley playing notes that glow the mist.
33
royal skyship emerging from clouds at sunset, wings made of gold leaf and wind.
34
A fanlasy tree sprouting glowing fruits under swirling aurora sky.
35
painting of desert nomad holding plowing hourglass, time swirls around their rohes. Hallowsen scares up 918 mn at global box office carns second highest borror opening of all time in North America. orbit Earth.
36
Space seady send first all-ciilian
38
Waterfall surrounded by nice early summer flowers. Heather Foothills, Mt. Hood Meudows ski area, Oregon.
39
The One And Only by Tim Walker for Vogue May 2014.
40
HD Wallpuper.
Veiled Within.
42
Stevens.
43
Man stands near waterfall.
deer made shimmering starlight grazing beside silver under purple sky. A crystal winged butterlly landing on dewdrop covered spiderweb in moonlit garden.
45
46
Milky way at the lake.
47
phoenix rising from ancient garden lountain, wings made of blooming petals and embers.
48
Fred I yon- San Francisco The Gallery at Leica Store San Francisco.
graffiti mural
wall saying 'ÀRT LIVES' in colorful spray-painee letters.
50
Newbern Baby Blanket Photography, Super Soft Photo. Basket Filler Basket Stuffer Prop.
neon street sign that says 'CyberCore Café', glowing in magentu blue.
52
An airship sail mid tear in storm, revealing the phrase 'WINDWRAITH" CREST' half-blow blown away.
53
A mugical sword embedded in stone, with the name "SOLARFANG" etched along blade.
54
A crow detective reading paper titled Feathered Conspiracies" headline in bold gothic script.
55
A stop sign with 'LLL WAY" written helow it. mechanical butterfly landing scroll that reads 'Silken Prophecy Delivered'. An otter with a laser gun.
57
bustling streets of Tokyo, crossouuss, beautiful girl sailoe suit riding on the back Asian elephant.
59
Sk resolution, realistic digital painting of colnssal dragon creature.
60
A dog swimming in space.
Whale Tail in water, award winning photo.
62
Inside a steampank workshop. a young cute redhead inventor, wearing blue overalls and a glowing blue tattoo on her shoulder.
Kayak in the water. optical color, acrial view, rainbow.
64
A loating mountain temple where monks ride beams of light to meditate among the stars, surrounded by glowing lotus clouds. celestial stag made lightning and auroras galloping across stormy sky, leaving trails stardust its wake.
40

---

Table 15: Comprehensive list prompts used across figures, experiments, and qualitative evaluations in the paper.
Prompt
sky harbor where airships dock on floating islands made of crystal, rainbow waterfalls cascading into the clouds. glowing portal the center of ancient eak tree guarded moss-covered stone wolves under violet twilight.
68
An underwater palacc lit by jellyfish lanterns, where merfolk in ornate armor bold council in coral throucs. firefly festival deep bamboo
spirit masks glowing A dragon curled around a mounlit lighthouse. its scales reflecting slars while waves crash below in silver mist. lihrary suspended
Blatiing
twilight.
70
floating books, glowing runes, staircases A snowy village where aurora borcalis woven into tapestries by mythical weavers in glowing fur robes. An enchanted canyon with floating stones engraved with prophecy, and golden birds nesting in the wird-carved cliffs.
shift every page
72
mermaid rocky shore, her tail shimmering with bioluminescent scales.
75
A warrior princsss brandishing crystal sword in the heart of a glowing battlefield. guardian golem
from emerald stone standing vigil ancient ruins.
77
A moonlit castle huilt atop waterfall that glows with bioluminescem algae.
floating island city above sea clouds with waterfalls cascading into mist.
79
A twilight marketplace staffed goblins selling glowing gemstones.
colossal treebridge sponning two mountain peaks under the aurora berealis.
of lavender with
flowers drifting toward distant spired city.
82
A ncon-lit lit dragonlly queen presiding over phosphorescent swamp.
crystal drugon coiled
an
lower under tapestry stars.
84
A marble statue of goddess that comes to life at dawn's first light.
hidden waterfall that pours rainbow mist crystal pool below.
41


Reviews:
[{"review_id": "YAARMJ6zPH", "reviewer": "Reviewer_SUK3", "summary": "This paper aims to address the shortcomings of current CFG methods, particularly in the context of rectified flow models. Specifically, traditional CFG approaches tend to extrapolate, which often leads to the generation of artifacts. In contrast, the authors observe that rectified flows favor interpolation. Based on this insight, they design a method that keeps the sample on the manifold using a predictor-corrector integrator framework. The paper provides theoretical analysis, along with detailed ablations and experiments across a wide range of models and benchmarks.", "questions": "NA", "limitations": "NA", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n- The paper is compared with CFG on a wide range of latest strong models such as Lumina, SD3, SD3.5, and FluxDEV, therefore prove the soundness of the proposed method. \n\n- It's interesting to see that the proposed method can improve text rendering ability, which is usually a bottleneck in latest image generation models.\n\n- The paper conduct evaluation on a wide range of commonly used benchmarks to support its claims, and the proposed method consistently outperforms or on par with the original CFG or other variants.\n\n- The proposed algorithm doesn't incur significant computational cost compared with the original CFG. Therefore, it's easy to be used as a plug-and-play module during inference. \n\nWeakness:\n\n- I didn't observe obvious weakness of this paper. It's well written and well supported by experiments. \n\n- In the tables, the author highlights almost all numbers, using colors like grey and orange, and also bolds the proposed method (Rect-CFG++). As a result, the presentation appears somewhat cluttered. It would be better to simplify the highlighting for improved clarity.", "was_revised": true, "final_justification": "Thank the authors for the rebuttal. I don’t have significant concerns about this paper. I’m not an expert in the theoretical aspects, so I’m not in a position to thoroughly evaluate that part. As for the experimental results, including the new ones provided in response to other reviewers, I don’t see any obvious flaws. Therefore, I will maintain my positive rating.", "rebuttal": "Dear Reviewer SUK3,\n\nThank you for your positive and encouraging review. **We are delighted that you found our paper to be technically solid, well-supported by experiments, and of high impact. We especially appreciate you highlighting the soundness of our method across a range of strong models, its ability to improve text rendering, and being well-supported by a strong theoretical foundation.**\n\nBelow, we address your point on presentation clarity.\n\n- **Regarding improving the presentation of tables and the use of colors:** We appreciate your feedback. As suggested, in the revised version of our paper, we will simplify table. This will ensure the key takeaways are presented in a much cleaner and more accessible manner.\n\nThank you again for your valuable feedback and strong support of our work. We are happy to answer any other questions you may have during the discussion phase. **Given that your concern is addressed, we humbly request that you consider increasing the score.**\n\nBest,\n\nAuthors of Submission #4997"}, {"review_id": "KGn4xnJ2N2", "reviewer": "Reviewer_iyy7", "summary": "This paper proposes an adaptive predictor-corrector guidance method for rectified flow-based models, combining the deterministic nature of rectified flows with a geometry-aware conditioning rule. During inference, the model first follows the conditional RF prediction, then applies a correction step between the conditional and unconditional velocity fields.", "questions": "Please refer to the weaknesses.", "limitations": "yes", "rating": 2, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "- Strengths\n    - This paper is well written and easy to follow.\n    - It introduces a novel, training-free methodology that improves efficiency.\n    - The paper constrains the extrapolative nature of CFG, bringing it closer to the target trajectory.\n- Weaknesses\n    - The paper should include a comparison with other geometry-aware guidance methods, such as CFG++ (Chung et al., 2024), which also addresses off-manifold issues. A more detailed discussion of how the proposed method relates to or differs from CFG++ in mitigating these challenges would strengthen the paper.\n    - The proposed method appears to be a variation of rectified flow that incorporates conditional updates. Since predictor-corrector (PC) schemes are already widely used in diffusion and flow-matching models, a clearer explanation is needed to distinguish this approach from existing PC-based sampling methods.\n    - The method appears sensitive to the guidance scale hyperparameter. It would be helpful to compare its performance against CFG under the same guidance scale setting.\n    - As the method is tailored to pre-trained flow-matching models, its generalizability and applicability to other model types remain questionable.", "was_revised": true, "final_justification": "Thank you for your detailed rebuttal. I have read it carefully and appreciate your response.\n\nHowever, the paper still lacks clear insights or comparisons that highlight the novelty of the predictor-corrector design over existing approaches. This raises concerns regarding the contribution, which remain unresolved. Therefore, I deduct one point.\n\nAdditionally, as shown in Table 1 and Table 3, the performance gain over w/CFG is relatively small.\n\nWhile the proposed method demonstrates good qualitative results, I find that the quantitative improvements and methodological contributions are not sufficiently compelling. Based on this, I am lowering my score to 2.", "rebuttal": "Dear Reviewer iyy7,\n\nThank you for your detailed and constructive feedback. We appreciate that you found our **paper well-written, our method novel and efficient, and that you recognized its core strength in constraining the extrapolative nature of CFG**. We address your concerns below:\n\n\n1. **Comparison with other geometry-aware guidance methods (e.g., CFG++):**  We appreciate the reviewer for highlighting the need for a clearer comparison with other geometry-aware methods like CFG++ (Chung et al., 2024). We would like to highlight that CFG++ is fundamentally incompatible with the rectified flow (RF) models.\n    - CFG++'s core mechanism involves modifying the renoising step in diffusion models after applying Tweedie's formula to the unconditional noise estimate (see Eq.4 in Algorithm-2 of CFG++). However, RF models are deterministic ODE-based, and do not have a re-noising process. Their sampling relies on an ODEUpdate step (Eq. 9) that integrates a velocity field. **Our method, Rectified-CFG++, modifies this velocity field (Eq. 8) before the ODE step, a fundamentally different approach. As also noted by Fan et al. (2025) in their work on CFG-Zero-Star, CFG++ is not designed for flow models and its direct application degrades to standard CFG.**\n    - For this reason, we focused our comparisons on methods that are more general, i.e. APG (Sadat et al., 2024) and CFG-Zero-Star (Fan et al., 2025). Our results demonstrate that Rectified-CFG++ consistently outperforms these state-of-the-art guidance strategies.\n\n**To better situate our work, we have added a detailed discussion of CFG++ in the revised Related Work section (**Sec. C.3 in Appendix**) to explicitly clarify these structural and algorithmic differences and justify our choice of baselines.**\n\n2. **Novelty compared to existing PC-based samplers:** We appreciate the reviewer for asking insightful question. While we adopt a predictor-corrector (PC) structure, our innovation lies in **how we purpose it for stable, multi-field guidance**, not merely for numerical accuracy. Standard PC samplers (e.g., Heun's method) are designed to improve the numerical integration of a single vector field. **In contrast, Rectified-CFG++ is a custom integrator designed to navigate between multiple vector fields (conditional and unconditional), importantly without deviating from the data manifolds. The key distinctions are:**\n    - The Predictor Step (Eq. 5): Our predictor is intentionally and purely conditional ( $v_t^c$ ​). This is critical for anchoring the trajectory to the learned data manifold at the beginning of each step. Using a mixed velocity here, as a standard PC sampler might, would reintroduce the very instability we aim to solve.\n    - The Corrector Step (Eq. 8): Our corrector is not a simple numerical average. It strategically combines the initial conditional velocity with a scheduled interpolation between the conditional and unconditional fields evaluated at the predicted midpoint. This adaptive, interpolative guidance signal is what provides robust, on-manifold correction.\n\n**We will revise Section 3.1 to make this novel formulation and its distinction from standard PC methods explicit.**\n\n3. **Sensitivity to guidance scale:** We apologize for the lack of clarity on this point. We would like to highlight and point reviewer that, our paper already provides a direct and extensive comparison of Rectified-CFG++ against standard CFG under identical guidance scale settings. **The results in Figure 9(a) and Tables 9 & 10 (Appendix) demonstrate the superior robustness of our method.** As shown below with an excerpt from Table 9, standard CFG's performance degrades sharply with increasing guidance, leading to a catastrophic drop in FID and ImageReward. **In contrast, Rectified-CFG++ maintains high performance and stability across the entire range of scales.**\n\n| Method | FID↓ / ImgRwd↑ (ω=3.0, λ=0.3) | FID↓ / ImgRwd↑ (ω=6.0, λ=1.0) | FID↓ / ImgRwd↑ (ω=10.0, λ=1.2) |\n| :--- | :---: | :---: | :---: |\n| CFG | 85.19 / 0.47 | 130.10 / -0.87 | 146.96 / -1.43 |\n| **Rect-CFG++**      | **74.66 / 1.00** | **75.40 / 1.02** | **76.17 / 1.04** |\n\n\n**This shows our method is significantly less sensitive to the guidance hyperparameter, a key advantage over standard CFG. We encourage reviewer to look at our detailed appendix where we have already provided experimental results and discussion in this regard.**\n\n\n4. **Generalizability to other model types:** We respectfully argue that specializing our method for rectified flow models is a deliberate design choice and a primary strength. The problem of off-manifold drift is particularly severe in deterministic ODE-based models, which lack the stochastic regularization inherent in traditional diffusion models. By tailoring our solution to the specific geometry of rectified flows, we developed a principled, highly effective approach that outperforms more generic, one-size-fits-all methods.\n\n    Given that leading foundation models like SD3, SD3.5, and Flux are now based on this paradigm, a specialized solution is both timely and impactful. **We believe a similar PC-guidance approach could be adapted for diffusion models and is a promising avenue for future work. One such way is to simply replace the unconditional and conditional velocities used in our method with the unconditional and conditional score estimates and use them to perform a PC update during each step of inference. Our focus was to solve a critical, unresolved problem in the emerging class of state-of-the-art flow-based generators.**\n\n\n**Formatting Concern (Year):** Thank you for catching this oversight in the template. We will correct the year to 2025 in the final version.\n\n\nWe hope these clarifications and our revisions have fully addressed your concerns. We are confident that these changes strengthen the paper, and we would be happy to answer any further questions during the discussion phase. **If you are satisfied with our rebuttal, we respectfully ask that you consider raising your score.**\n\n\n\n[1] Hyungjin Chung, Jeongsol Kim, Geon Yeong Park, Hyelin Nam, and Jong Chul Ye. Cfg++: Manifold constrained classifier free guidance for diffusion models. arXiv preprint arXiv:2406.08070, 2024\n\n[2] Weichen Fan, Amber Yijia Zheng, Raymond A Yeh, and Ziwei Liu. Cfg-zero*: Improved classifier-free guidance for flow matching models. arXiv preprint arXiv:2503.18886, 2025.\n\n[3] Seyedmorteza Sadat, Otmar Hilliges, and Romann M Weber. Eliminating oversaturation and artifacts of high guidance scales in diffusion models. In The Thirteenth International Conference on Learning Representations, 2024\n\n\nBest regards,\n\nAuthors of Submission #4997"}, {"review_id": "ynyPmMgzWu", "reviewer": "Reviewer_ZP1S", "summary": "The paper proposes Rectified-CFG++, a predictor-corrector based adaptive guidance method for diffusion models that combines rectified flows with manifold-aware conditioning. The authors claimed that it ensures stable and efficient sampling by anchoring updates near the data manifold and interpolating between conditional and unconditional velocity fields. Experimental results are provided to show that the method outperforms standard CFG across multiple large-scale models and benchmar", "questions": "Q1: Validity of Theoretical Claims -- \nAs discussed above, the current theoretical analysis does not sufficiently support the claim that the proposed method ensures manifold-constrained sampling. Lemma 3.1 and Proposition 1 merely suggest bounded deviation of the sampling path, which is not equivalent to alignment with the true data manifold. To rigorously validate this claim, the authors are encouraged to provide a more formal analysis—e.g., by examining whether the proposed sampling scheme satisfies the continuity equation or the Kolmogorov Forward Equation (KFE). Such analysis would clarify whether the proposed predictor–corrector framework preserves the desired data distribution over time and substantiate its theoretical contribution.\n\nQ2: Ambiguity and Lack of Clarity in Figure 1 --\nThe current version of Figure 1 and its caption are ambiguous and uninformative. It is unclear what specific problem in existing methods the figure is intended to highlight, or how the proposed method addresses it. The visual does not clearly convey either the failure mode of standard CFG or the geometric benefit introduced by Rectified-CFG++. The authors should revise this figure to more clearly illustrate the motivation, contrast the behavior of existing vs. proposed approaches, and explicitly indicate what the readers should take away from it.", "limitations": "yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "**Strengths**\nAlthough the manifold constrained CFG has been proposed for diffusion models, it has not been exploited for rectified Flow model. Given the subtle and important differences between the rectified flow and diffusion, the scope of the paper is timely and could be potentially impactful.  Moreover, idea of using predictor and correct sampling, which is an important sampling scheme in flow and diffusion, for the CFG correction is also intriguing.\n\n**Weaknessess**\nAlthough the reviewer agrees that employing a predictor–corrector sampling framework is a promising direction for improving classifier-free guidance (CFG), the current manuscript does not convincingly validate this approach. In particular, while the authors emphasize theoretical contributions through Lemma 3.1 and Proposition 1, these results appear insufficient to support the claim that the proposed method performs manifold-constrained sampling. At best, they suggest that the sampling trajectories do not diverge excessively—but this does not imply that the trajectories accurately follow the data manifold. To rigorously demonstrate that the predictor–corrector scheme induces samples along the true data manifold, it would be more appropriate to analyze whether the resulting trajectories satisfy a continuity equation or the Kolmogorov Forward Equation (KFE) [1], which describe the evolution of probability densities under the stochastic process. Without such theoretical grounding, the core claim of geometry-aware sampling remains speculative. This lack of formal validation undermines the strength of the manuscript’s theoretical contributions and leaves the reviewer uncertain about the true efficacy of the proposed method.\n\n[1] Lipman, Yaron, et al. \"Flow matching guide and code.\" arXiv preprint arXiv:2412.06264 (2024).", "was_revised": true, "final_justification": "With the remaining theoretical resolved, the reviewer increases the rating to 4.", "rebuttal": "Dear Reviewer ZP1S,\n\nThank you for your insightful review. We appreciate your engagement with our work and your acknowledgment that the scope of our paper is timely and impactful, and that our work is of high significance. We address your concerns below:\n\n1. **Validity of Theoretical Claims:** We appreciate the reviewer's insightful feedback regarding the theoretical grounding of our manifold-constrained sampling claim. Our core claim is that Rectified-CFG++ has stronger adherence to the learned data manifold. Lemma 3.1 and Proposition 1 demonstrate bounded single-step perturbation and stability of the predicted guidance direction, which sufficiently proves the preservation of the desired data distribution. Here, we provide a more direct argument for how Rectified-CFG++ implicitly maintains better consistency with the desired KFE through its manifold-aware design.\n\n    - **The Challenge of Off-Manifold Dynamics in Standard CFG:** In deterministic rectified flows, the underlying process is governed by an ODE with a learned velocity field. The evolution of the probability density function $\\rho(x,t)$ for this process is described by the continuity equation, a form of the KFE [2]:\n            $$\\frac{\\partial \\rho(x,t)}{\\partial t} = -\\nabla \\cdot [v_t(x)\\rho(x,t)]$$\n        For a well-trained rectified flow model, the learned conditional $v_t^c(x)$ and unconditional $v_t^u(x)$ velocity fields are implicitly designed to be tangent to their respective data manifolds at time $t$. Standard CFG, by linearly combining the conditional and unconditional velocity fields, fundamentally introduces an issue. When the guidance scale $\\omega > 1$, this operation becomes an extrapolation [1]. Since this may not have been apparent, we now explain this explicitly in the paper. \n        - **Formal Implication of Extrapolation for KFE Violation:** Extrapolating the velocity field (effective velocity in standard CFG), especially on piecewise linear manifolds, can push it beyond the data manifold's tangent space. The resulting velocity vector points into low-density regions of the latent space, away from the true data distribution.\n        - **Disruption of Probability Flow:** Consequently, the probability flow described by the KFE is also driven off-manifold. This \"leakage\" of probability mass into invalid areas violates the core assumption that the data distribution remains on its manifold. This directly causes generative artifacts and results in an incoherent and unfaithful evolution of the data distribution.\n    - **Rectified-CFG++ & On-Manifold KFE Dynamics:** Rectified-CFG++ directly addresses this by restructuring the guidance application within a predictor-corrector framework (Algorithm 1) to ensure the effective velocity field maintains manifold proximity, leading to a more consistent KFE-driven probability evolution.\n\n        - **Argument for On-Manifold Evolution and KFE Consistency:** (**Predictor as Manifold Anchor) The first step in Rectified-CFG++ is the conditional predictor update (Algorithm 1, Line 4):\n                $$x^1_{t-\\Delta t/2} \\leftarrow x_t + \\frac{\\Delta t}{2} v_t^c$$ Since $v_t^c$ is the learned conditional velocity field, it is specifically trained to be tangent to the conditional data manifold $M_{t|y}$ at $x_t$ (as per Equation A.1, Lemma A.1 in our Appendix). This predictor step ensures that the intermediate sample $\\tilde{x}_{t-\\Delta t/2}$ is directly moved along the learned manifold's trajectory. By initiating each step with a manifold-tangent movement, we effectively \"anchor\" the sample to the manifold, preventing an immediate departure from the high-density regions of the data distribution. This means that the probability density, at this predictive sub-step, is explicitly evolved along the manifold's natural flow, consistent with the KFE.\n\n        (**Corrector as Manifold-Aware Controlled Correction**) The subsequent corrector step (Algorithm 1, Line 8, and Equation 8) is the core of our geometry-aware conditioning. Crucially, the guidance difference term ($v_{t-\\Delta t/2}^c(x^1_{t-\\Delta t/2}) - v_{t-\\Delta t/2}^u(x^1_{t-\\Delta t/2})$) is computed by evaluating both the conditional and unconditional velocities at the manifold-proximate predicted point $x^1_{t-\\Delta t/2}$. Since $x^1_{t-\\Delta t/2}$ is on or very close to the manifold $M_{t-\\Delta t/2}$, both $v_{t-\\Delta t/2}^c(x^1_{t-\\Delta t/2})$ and $v_{t-\\Delta t/2}^u(x^1_{t-\\Delta t/2})$ are (approximately) tangent to the respective manifolds at that location. As proven in our Lemma A.1 (L431-433), the linear combination of these manifold-tangent vectors inherently results in an effective velocity $\\hat{v}_{\\lambda, t}$ that largely remains within the tangent space of the next-step conditional manifold or its immediate tubular neighborhood. This is fundamentally different from standard CFG's extrapolation from a single point, which can push trajectories far off the manifold.\n\n        - **Preservation of KFE Manifold Support:** Our Proposition 1 (L159-165) formally quantifies this, stating that the per-step deviation of the Rectified-CFG++ trajectory from the pure conditional path is bounded. This directly implies that the probability density $\\rho(x,t)$ evolving under the Rectified-CFG++'s effective velocity primarily flows close to the conditional data manifold. While it is true the KFE for a guided process ($\\frac{\\partial \\rho(x,t)}{\\partial t} = -\\nabla \\cdot [\\hat{v}_{\\lambda,t}(x) \\rho(x,t)]$) describes a modified evolution, in standard CFG this is unconstrained, and thus frequently goes off-manifold, whereas in our case the evolution is better constrained on the manifold. This ensures that the generated samples consistently correspond to valid, high-probability data configurations.\n\n- **Implications for Artifact Avoidance:** By explicitly ensuring that the sampling trajectory adheres closely to the learned data manifold throughout the reverse process, Rectified-CFG++ inherently prevents the generation of artifacts. The \"color blow-outs, warped geometry, and hyperparameter sensitivity\" (L41) observed with standard CFG directly result from operating in regions of the latent space that do not correspond to meaningful data. By keeping the probability flow on-manifold, Rectified-CFG++ maintains the intrinsic visual coherence, semantic fidelity, and structural integrity of the generated images, as visually demonstrated in Fig. 1 (Top), Fig. 2 (Right), and Fig. 3. This manifold-aware evolution, grounded in maintaining KFE consistency on the data manifold, is key to our method's superior performance.\n\n**Exact satisfaction of KFE: As noted on page-34 of the paper cited by the reviewer by Lipman et al. [2], for guided velocities, the exact form of the probability distribution is unknown, so a KFE cannot be verified in its exact form. Given the absence of any kind of rigorous theory in the literature, we provide an approximate analysis following [3-5] to show that our method has better fidelity to the conditional manifold. In fact, strict satisfaction of the KFE may even be detrimental, since it would imply exactly pushing to the conditional data distribution, which leads to loss of sample diversity.**\n\n**We will significantly revise Section 3.2 to feature the result from Lemma A.1 more prominently. We will also add the above explanation for more rigour theoretical guarantees along with a more formal proof.**\n\n2. **Lack of Clarity in Fig. 1:** We thank the reviewer for highlighting the clarity issue in Fig.1. We take this opportunity to explain Figure 1 here and will update the figure in our manuscript.\n    - **Visual Comparison (Top Row):** We aimed to show that standard CFG produces both structural and color artifacts. In the example, standard CFG distorts the paddle into an unnatural cross-shape fused with the person and renders a small, misplaced rainbow. Our method correctly renders a distinct paddle and a large, smoothly blended rainbow that aligns with the prompt.\n    - **Conceptual Manifold Diagram (Bottom Row):** The diagram is meant to provide the geometric intuition for why these artifacts occur. The standard CFG path (blue) deviates from the learned manifold $M_t$, while our method's path (green) stays aligned. We will make it more explicit. We will add clear labels for the manifold ($M_t$), the tangent space ($T_{x_t}M_t$), and the velocity vectors ($v^c, v^u, \\Delta v$). This will visually illustrate how the extrapolated CFG vector pushes the blue trajectory out of the tangent space, whereas our predictor-corrector steps keep the green trajectory aligned with the manifold's geometry.\n\nWe will rewrite the caption to be a clear, step-by-step guide that walks the reader through these new visual cues, ensuring the figure's motivation and our method's benefit are immediately apparent.\n\nWe are confident that these minor revisions will fully address your primary concerns. **We sincerely request that you re-evaluate and consider raising the overall score.**\n\n\n[1] Hyungjin Chung, Jeongsol Kim, Geon Yeong Park, Hyelin Nam, and Jong Chul Ye. Cfg++: Manifold constrained classifier free guidance for diffusion models. arXiv preprint arXiv:2406.08070, 2024\n\n[2] Lipman, Yaron, et al. \"Flow matching guide and code.\" arXiv preprint arXiv:2412.06264 (2024).\n\n[3] Sander Dieleman. Guidance: a cheat code for diffusion models, 2022. https://benanne.github.io/2022/05/26/ guidance.html\n\n[4] Yingqing Guo, Hui Yuan, Yukang Yang, Minshuo Chen, and Mengdi Wang. Gradient guidance for diffusion models: An optimization perspective. arXiv preprint arXiv:2404.14743, 2024.\n\n[5] Muthu Chidambaram, Khashayar Gatmiry, Sitan Chen, Holden Lee, and Jianfeng Lu. What does guidance do? a fine-grained analysis in a simple setting. arXiv preprint arXiv:2409.13074, 2024.\n\n[6] Arwen Bradley and Preetum Nakkiran. Classifier-free guidance is a predictor-corrector. arXiv preprint arXiv:2408.09000, 2024.\n\nBest,\nAuthors of Submission #4997"}, {"review_id": "BjOVfNQpQQ", "reviewer": "Reviewer_sxp4", "summary": "This paper proposes an improved Classifier-Free Guidance for Flows. The primary objective of paper is to enhance the quality of image generation for flow models. It provides both theoretical and practical evidence.", "questions": "Q1: As I understand it, the proposed method effectively converts the previous single-step process into a multi-step procedure. To elaborate, if the CFG runs for 20 timesteps, it would involve the model being invoked 40 times. In contrast, under the method presented in this paper, running for 20 timesteps would require the model to be invoked 60 times. Could the authors please confirm whether my calculation is accurate in this regard?\n\nQ2:  Whether the quantitative and qualitative experiments conducted in this paper were carried out under the same number of timesteps. If the calculation in Q1 is right, it seems that for a fair comparison, the CFG method should be evaluated with twice the number of timesteps. \n\nQ3: In Table 4, the evaluation is based on the number of sampling steps (NFEs). I am curious to know what the results would look like if the evaluation criterion were changed to the number of times the flow model is called instead. \n\nQ4: In line 5 of Algorithm 1, a random noise is added. Is there no coefficient needed for this random noise? Is this random noise enabled in this paper? Will the introduction of this randomness disrupt the manifold that the paper aims to pursue?\n\nQ5: Proposition 1 proves that there exists an upper bound, which ensures that the trajectory remains boundedly close to the target conditional flow path. This is fine. However, how does this ensure artifact reduction? Being close to the target conditional flow path doesn't seem to explain it. If I simply lower the CFG value, it will naturally be closer. Compared to directly adjusting the CFG value, what is the advantage of this paper?", "limitations": "Yes", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 4, "originality": 3, "strengths_and_weaknesses": "### Strengths\n\n1, The method proposed in this paper is easy to understand and reproduce. Additionally, the authors provide the code.\n\n2, This paper improves upon state - of - the - art generative models and has significant frontier value.\n\n3, The paper provides abundant visual results, which are of high quality, effectively demonstrating the method's potential and reliability.\n\n### weaknesses\n\n1, Based on my understanding, the original process involves a timestep going through the neural network **twice**. \nThe proposed method changes this to a process where a timestep goes through the neural network **three times**.\nGiven this understanding,  the comparison experiment may not be fair.\n\n2,The primary contribution of this paper is to provide image details while suppressing artifacts. However, the paper lacks theoretical proof for artifact reduction. More details see Q5.\n\n3, The method consumes more time under identical conditions, which may restrict its practical application.", "was_revised": true, "final_justification": "Judging from the new table provided by Rebuttal, this article has improved efficiency. In addition, the mechanism of this article is worth studying. These advantage prompted me to increase the score.", "rebuttal": "Dear Reviewer sxp4,\n\nThank you for your constructive review and positive feedback. We are delighted that you found our **method easy to understand, our results compelling, and our paper's direction to be of significant frontier value**. We address your concern below:\n\n1.  **Computational Cost and Fairness of Comparison:** This is a critical point, and we appreciate you raising it. \n\n    **(Q1) Your calculation is correct:** our method uses 3 model evaluations per step (NFE), whereas standard CFG uses 2. The core of our contribution, however, is that **Rectified-CFG++ is significantly more efficient per model call, achieving superior results for a comparable or even smaller total computational budget.** \n\n    **(Q3)** To address your question directly, we have reframed the comparison to be based on total model calls and runtime, which we believe is the fairest measure of computational cost.\n\n\n    | Guidance | Total Model Calls | Runtime (s) | FID (↓) |\n    | :--- | :---: | :---: | :---: |\n    | CFG | 28 NFEs * 2 = 56 | 5.31s | 85.82 |\n    | **Rect.-CFG++**    | **20 NFEs * 3 = 60** | **5.35s** | **74.47** |\n\n\n    **(Q2)** Please note that in Table 4, we tried to keep the comparison as close as possible for all parameters, making sure the runtime and model calls are close. Our method achieves a better FID score in just 20 steps (60 model calls) compared to the standard CFG, requiring 28 steps (56 model calls). The total number of model calls is nearly identical (60 vs. 56), and the inference runtime is also virtually the same (5.35s vs. 5.31s), yet our method delivers higher quality (see **Table 11**). This demonstrates a superior quality-per-computation trade-off (**We follow the same setting throughout in the paper**). \n\n   **We also highlight that Reviewer SUK3 independently reached a similar conclusion, finding our computational cost to be comparable. Furthermore, our NFE ablation studies (Tables 11, 12, 13 in the Appendix) show that our method converges much faster. For instance, with the Flux model (Table 11), our method achieves an FID of 71.17 in just 5 NFEs (15 model calls), a score standard CFG fails to reach even after 60 NFEs (120 model calls). We encourage and request the reviewer to please look at the detailed appendix sections.**\n\n**We will revise Section 4.2 (Computational Efficiency) to state this more explicitly.**\n\n\n\n2.  **Random Noise in Algorithm 1:** This is an excellent question regarding Line 5. There is indeed a typo here, and there should be a hyperparameter to add extremely small noise (**it does not affect the manifold**); we have corrected it in our updated manuscript. Introducing a small amount of stochasticity helps explore the solution space. However, to ensure a direct and fair comparison with the standard CFG, all experiments reported in this paper were conducted without this optional noise term. We would like to highlight that this small noise does affect the overall performance. \n\n\n\n3.  **Theoretical Proof for Artifact Reduction:** Thank you for this fundamental and insightful question. \n\n \n    - **Standard CFG**: Artifacts arise when a high guidance scale ($\\omega$) pushes the sampling trajectory far off the learned data manifold. In these off-manifold regions, the model's learned velocity field is unreliable, leading to artifact generation. **The naive solution is to simply lower the CFG scale. However, this severely weakens prompt alignment, making images generic and unfaithful to the text prompt. This creates a poor trade-off: you must choose between fidelity and alignment.**\n\n    - Rectified-CFG++ resolves this dilemma.**It uses a strong guidance signal (the difference term) but applies it via a manifold-aware interpolation rather than extrapolation. As proven in Proposition 1 and further supported by our KFE-based analysis (see rebuttal to Reviewer ZP1S), our method's bounded deviation ensures the trajectory remains in a tight \"tubular neighborhood\" of the data manifold. By staying on the manifold, the velocity field remains reliable, which directly prevents the large off-manifold excursions that cause artifacts. Unlike just lowering the CFG scale, our method preserves a strong guidance signal via the interpolated difference term. This allows us to achieve strong prompt fidelity simultaneously with high image quality.** \n\n    This ability to maintain high alignment without quality collapse is empirically proven in Figure 9(a), which shows our method remains stable and effective at guidance scales where standard CFG's quality collapses entirely.\n\nWe will revise the explanation in our paper to further clarify the distinction from simple CFG value change and the advantages of our method. We will also clarify how this mechanism breaks the alignment-fidelity trade-off, which is the primary advantage over simply lowering the CFG scale.\n\n**Formatting Concern (Year):** Thank you for catching this oversight in the template. We will correct the year to 2025 in the final version.\n\nWe are confident that these clarifications will fully address your concerns. We would be happy to answer any further questions during the discussion phase. **If you are satisfied with our rebuttal, we respectfully ask that you consider raising your score.**\n\nBest,\n\nAuthors of Submission #4997"}]

Author rebuttal:

Meta-review: Authors present an adaptive predictor–corrector guidance method for rectified flow models. The work addresses some weakness of standard classifier-free guidance, namely off-manifold drift, and combines theory with good empirical validation across multiple state-of-the-art models. Some concerns remain about novelty relative to existing predictor–corrector schemes and about the depth of the theoretical justification. While these points are valid, the authors provided some clarifications and additional proofs during the rebuttal, and the experimental results are at minimum consistent. AC recommend a weak accept.
Decision: Accept (poster)