Correlation Analysis of Generative Models

Zhengguo Li; Chaobing Zheng; Wei Wang

cs.LGFeb 20, 2026

Correlation Analysis of Generative Models

Authors: Zhengguo Li, Chaobing Zheng, Wei Wang

Organizations: VI Department, Institute for Infocomm Research, A*STAR, Singapore, 138632 · School of ISE, Wuhan University of Science and Technology, Wuhan, China · School of CST, Wuhan University of Science and Technology, Wuhan, China

Abstract

Based on literature review about existing diffusion models and flow matching with a neural network to predict a predefined target from noisy data, a unified representation is first proposed for these models using two simple linear equations in this paper. Theoretical analysis of the proposed model is then presented. Our theoretical analysis shows that the correlation between the noisy data and the predicted target is sometimes weak in the existing diffusion models and flow matching. This might affect the prediction (or learning) process which plays a crucial role in all models.

Figures & tables

	diffusion model in [ 2 , 10 ]	diffusion model in [ 3 , 11 ]	models in [ 20 , 21 ]	Trigflow in [ 5 ]	flow matching in [ 4 ]
$a_{11}(t)$	$\alpha_{t}$	$\alpha_{t}$	$\frac{\sigma_{d}}{\sqrt{\sigma_{d}^{2}+t^{2}}}$	$\cos(t)$	$1-t$
$a_{12}(t)$	$\sigma_{t}$	$\sigma_{t}$	$\frac{t}{\sqrt{\sigma_{d}^{2}+t^{2}}}$	$\sin(t)$	$t$
$a_{21}(t)$	$0$	$1$	$a_{12}(t)$	$-a_{12}(t)$	$-1$
$a_{22}(t)$	$1$	$0$	$-a_{11}(t)$	$a_{11}(t)$	$1$
$\|A(t)\|$	$\alpha_{t}$	$-\sigma_{t}$	$-1$	1	1
$\Psi_{X_{t},\omega}$	$\sigma_{t}$	$\alpha_{t}$	0	0	$\frac{2t-1}{\sqrt{2((t-1)^{2}+t^{2})}}$

TABLE I: Theoretical analysis of existing diffusion models and flow matching. For simplicity, the deterministic method in [ 22 ] is chosen for illustration.

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Flow Matching (FM) is a simulation-free method for learning a continuous, invertible flow that interpolates between two distributions, and in particular generates data from noise. Inspired by the variational nature of the diffusion process as a gradient flow, we introduce a stepwise FM model, Local Flow Matching (LFM), which sequentially learns a sequence of FM submodels, each matching a diffusion process up to the time-step size in the data-to-noise direction. In each step, the two distributions to be interpolated by the sub-flow model are closer than those in the full-flow matching model, which interpolates data to noise distributions, enabling smaller models with more efficient training. This variational perspective also allows us to prove a theoretical generation guarantee for the proposed flow model in terms of the

χ^2

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