Flat-Consensus Diffusion for Robust Data Reshaping under Noisy Evaluator

Hongyu Cao; Kunpeng Liu; Fei Xie; Sandip Ray

cs.AISep 26, 2026

Flat-Consensus Diffusion for Robust Data Reshaping under Noisy Evaluator

Authors: Hongyu Cao, Kunpeng Liu, Fei Xie, Sandip Ray

Organizations: Clemson University Clemson, SC, USA · Portland State University Portland, OR, USA · University of Florida Gainesville, FL, USA

Abstract

Data shape determines how features are structured, how patterns are separated, and how distributions cover the underlying domain. Poor data shape can make models learn noise rather than generalizable structure. This paper studies robust feature-centric data reshaping: generating feature transformations that remain useful, stable, and reproducible under noisy evaluation and imperfect data conditions. We view reshaping operation sequence search as reward-guided diffusion generation, and robust reshaping as searching for regions in the latent reward landscape rather than isolated high-reward transformations. The key challenge is dual instability: noisy evaluators distort local reward guidance, while stochastic generative trajectories can converge to inconsistent solutions. We propose FCDiff, a flat-consensus diffusion framework that addresses both failures through a micro-macro decomposition. The micro layer replaces point-estimate reward guidance with Gaussian-smoothed, Monte Carlo averaged gradients, steering generation toward locally flat reward regions. The macro layer aggregates independently guided trajectories with a weighted Frechet-mean barycenter, selecting consensus-supported basins and filtering stochastic outliers. Across an 8-dataset headline cohort under heavy-tailed evaluator noise, FCDiff attains the best aggregate rank on lower-tail reliability and robustness against both search-based AutoFE and robustness-oriented generative baselines, with statistically significant accuracy gains over every generative baseline. Our results show that robust data reshaping requires searching for flat, consensus-supported regions rather than sharp single-trajectory optima.

Figures & tables

Fig. 1 : Robust data reshaping at a glance: two coupled instabilities. (a) Evaluator noise. Search runs over a latent reward landscape scored by a noisy evaluator (gray band); under a small latent perturbation

\pm\delta

, a sharp peak loses its reward while a flat region keeps it. (b) Trajectory stochasticity. Independent guided trajectories from the same noise

z_{T}

end at different latents; we aggregate them into a weighted consensus (star) that down-weights stochastic outliers. FCDiff targets regions that are both flat and consensus-supported.

Fig. 2 : FCDiff as a symmetric micro–macro framework for robust data reshaping. A VAE–reward–diffusion backbone builds a continuous latent reward geometry over discrete reshaping sequences. The micro layer handles local reward instability by smoothing point-estimate guidance into flat-region guidance. The macro layer handles trajectory-level instability by aggregating multiple guided endpoints into a consensus latent. Together, FCDiff searches for flat, consensus-supported regions rather than sharp single-trajectory optima.

	Micro (Local)	Macro (Global)
Failure Mode	Noisy reward gradients	Stochastic trajectory divergence
Operator	Gaussian smoothing	Fréchet mean aggregation
Objective Relaxation	$R(z)\rightarrow\mathbb{E}_{\delta}[R(z+\delta)]$	$\max\rightarrow$ consensus center
Geometry	Flat regions	Broad basins
Effect	Reduces local sensitivity	Reduces cross-run variance
Output	Stable trajectory endpoint	Consensus latent solution

TABLE I : Structural symmetry of the micro and macro components in FCDiff. The two layers address complementary sources of instability and jointly enable region-level robust reshaping.

		ml_586			ml_589			ml_607			ml_620
Group	Method	Perf.	CVaR	Worst	Perf.	CVaR	Worst	Perf.	CVaR	Worst	Perf.	CVaR	Worst
Search	RL	0.682	0.662	0.662	0.678	0.662	0.662	0.666	0.651	0.651	0.660	0.647	0.647
	Evo	0.698	0.658	0.658	0.691	0.652	0.652	0.688	0.661	0.661	0.657	0.638	0.638
	LLM	0.688	0.654	0.635	0.685	0.664	0.639	0.666	0.659	0.658	0.656	0.640	0.638
Robust-gen	Std	0.687	0.684	0.683	0.674	0.671	0.671	0.663	0.659	0.658	0.652	0.652	0.652
	Adv	0.687	0.683	0.683	0.674	0.671	0.671	0.663	0.659	0.659	0.652	0.650	0.650

TABLE II : Main results (8-dataset headline cohort, 3 metrics: Perf., CVaR@5, Worst). All methods optimise under Student-

t(\nu{=}3,\sigma{=}1)

noise on every reward query; downstream performance reported on the clean 5-fold CV evaluator (

1\!-\!

RAE for the four ml_* regression datasets, macro-F1 for spectf / svmgd3 / spam / ap_omn ). Search baselines:

n{=}5

pipelines; robust-gen + Ours : up to

n{=}100

/dataset. Per-cell global winners bolded (ties bolded jointly). The per-cell deltas look small, but they are systematically in Ours’ favour: 13/24 per-cell wins (incl. ties), and statistically separable from every robust-gen baseline on Perf. (paired Wilcoxon,

p\!<\!0.05

n{=}8

); full statistics in § IV-B .

	Mean rank (1 = best)			$p$ (vs FCDiff)
Method	Perf.	CVaR@5	Worst	Perf.	CVaR@5	Worst
FCDiff (ours)	2.25	2.00	3.12	—	—	—
Std-Diff	4.88	3.25	3.25	.008	.203	.438
Adv-PGD	5.88	4.75	4.25	.008	.016	.125
Grad-Clip	5.25	4.88	4.88	.008	.016	.031
Medoid-Cons	7.00	5.25	5.00	.008	.008	.094

TABLE III: Aggregate reliability summary across the 8-dataset headline cohort. Mean rank is averaged over the 8 datasets within each metric (1 = best, 8 = worst). p (vs FCDiff) is the two-sided paired Wilcoxon signed-rank test on the per-dataset deltas. Bold = best mean rank in column; p bolded when

p\!<\!0.05

. FCDiff attains the lowest mean rank on every metric, with statistically significant gains across the four robust-gen baselines on Perf. and CVaR@5; the Worst-metric tie with Std-Diff is the regime in which both methods occupy the same single-trajectory peak, while CVaR@5 separates them.

Panel of Figure 6 — Fig. 3 : Diagnostics for the micro and macro layers (cohort: 3-dataset SDEdit-init side cohort in (a)(b); 8-dataset headline cohort in (c)).

Panel of Figure 7 — Fig. 4 : Geometry (RQ5) and efficiency (RQ6) diagnostics.

	Worst-10% Utility ( $\uparrow$ )			Utility Var. ( $\downarrow$ , $\times 10^{-4}$ )
Variant	586	spectf	svm3	586	spectf	svm3
DIFFT (Std-Diff, $K{=}M{=}1$ )	0.729	0.500	1.103	2.6	2.7	140
+ smoothing ( $K{>}1$ , $M{=}1$ )	0.731	0.806	2.171	0.98	0.55	53
+ consensus ( $K{=}1$ , $M{>}1$ )	0.743	0.545	1.833	0.75	0.89	20
FCDiff (both layers)	0.748	0.845	2.361	0.52	0.66	15

TABLE IV : DIFFT-backbone head-to-head on the SDEdit-anchored side cohort (3 datasets where the variants admit clean discrimination). DIFFT (Std-Diff) is the vanilla DIFFT backbone with

K{=}M{=}1

from Table II ; the other rows add one or both of our ensemble layers. Numbers are mean over 20 seeds

\times

50 samples per cell. Worst-10% Utility : surrogate-space lower tail (higher = better). Utility Var. : per-trajectory utility dispersion (lower = better), reported in units of

10^{-4}

. The (syntactic) invalid-decode rate is

0.0

for all four variants on all three datasets of this SDEdit-anchored cohort and is therefore omitted from the table. Per-cell winners are bolded .

Method	ml_586	spectf	svmgd3	spam	Decode valid
best-of- $M$	.727	.771	.859	.957	100%
consensus	.745	.798	.875	.961	100%
$\Delta$ (cons. $-$ best-of- $M$ )	+.018	+.027	+.016	+.004	—

TABLE V : Consensus latent vs. best-of-

M

(

M{=}20

50

seeds, Student-

t(\nu{=}3,\sigma{=}1)

). Cells report Worst-10% Utility (higher is better). Syntactic decode validity is identical (and perfect) for both on every dataset; consensus dominates on the tail metric, with the gap shrinking toward zero on easy datasets where reward noise has minimal effect on best-of-

M

Variant	586	589	607	620	spectf	svm3	spam	ap_om
Worst-10% Utility (higher = better)
full_FCDiff	1469.1	360.5	1962.2	1002.6	1.14	494.2	1522.6	7.0
standard_M	40.0	5.2	20.4	13.1	0.93	11.0	14.0	2.4
single_FCDiff	1351.8	322.0	1852.4	930.8	1.07	433.8	1417.1	4.4
Wall-clock (s, lower = faster)
full_FCDiff	58.8	59.8	60.0	49.1	23.0	48.7	59.5	57.6

TABLE VI : Compute-matched comparison at

M{=}16

on the 8-dataset headline cohort (this slice is from the RQ6

M

-sweep

\{4,8,16,32\}

; the headline ablation uses

M{=}20

). Best-of-

M

( standard_M ) and single guided trajectory ( single_FCDiff ) are matched-compute baselines for the consensus output ( full_FCDiff ). Per-cell winners on the Worst-10% Utility row are bolded .

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