Analyzing and Mitigating Model Collapse in Rectified Flow Models

TL;DR

The paper addresses MC in diffusion/flow models trained with self-generated data, focusing on Rectified Flow and its Reflow procedure. It provides a theoretical MC analysis by studying a linear Denoising Autoencoder subjected to recursive self-training, linking collapse mechanisms to diffusion/Rectified Flow, and proves that introducing real data can prevent collapse. The authors then propose Real-data Augmented Reflow (RA Reflow) and online variants (ORA Reflow, ORAS Reflow) that blend real reverse noise–image pairs with synthetic data to straighten flows while preserving stability. Empirical results on Gaussian tasks and standard image benchmarks (CIFAR-10, CelebA-HQ) show that RA/ORA/ORAS Reflow mitigates MC and achieves high-quality sampling with fewer function evaluations. The work advances understanding of MC in simulation-free generative models and offers practical, data-efficient strategies to maintain sampling efficiency in Rectified Flow.

Abstract

Training with synthetic data is becoming increasingly inevitable as synthetic content proliferates across the web, driven by the remarkable performance of recent deep generative models. This reliance on synthetic data can also be intentional, as seen in Rectified Flow models, whose Reflow method iteratively uses self-generated data to straighten the flow and improve sampling efficiency. However, recent studies have shown that repeatedly training on self-generated samples can lead to model collapse (MC), where performance degrades over time. Despite this, most recent work on MC either focuses on empirical observations or analyzes regression problems and maximum likelihood objectives, leaving a rigorous theoretical analysis of reflow methods unexplored. In this paper, we aim to fill this gap by providing both theoretical analysis and practical solutions for addressing MC in diffusion/flow models. We begin by studying Denoising Autoencoders and prove performance degradation when DAEs are iteratively trained on their own outputs. To the best of our knowledge, we are the first to rigorously analyze model collapse in DAEs and, by extension, in diffusion models and Rectified Flow. Our analysis and experiments demonstrate that rectified flow also suffers from MC, leading to potential performance degradation in each reflow step. Additionally, we prove that incorporating real data can prevent MC during recursive DAE training, supporting the recent trend of using real data as an effective approach for mitigating MC. Building on these insights, we propose a novel Real-data Augmented Reflow and a series of improved variants, which seamlessly integrate real data into Reflow training by leveraging reverse flow. Empirical evaluations on standard image benchmarks confirm that RA Reflow effectively mitigates model collapse, preserving high-quality sample generation even with fewer sampling steps.

Figures (7)

• Figure 1: Two Scenarios for Studying Model Collapse.Top: Rectified Flow uses the Reflow method, iteratively relying on self-generated data to straighten the flow and improve sampling efficiency. Left: Model collapse occurs when models are repeatedly trained on their own outputs, progressively degrading performance. Right: Adding real data at each iteration mitigates collapse by preserving sample quality. Bottom: Visualization of correction streams after 10 iterations. The baseline lacks color and produces blurry, mixed outputs, whereas our approach maintains clarity and fidelity.
• Figure 2: 2D multi-Gaussian experiment demonstration.(A) Rectified Flow rewires trajectories to eliminate intersecting paths, transforming from $(a)$ to $(b)$. We then take noise samples from the distribution $p^z$ and their corresponding generated samples from the synthetic distribution $p_1^x$ to construct noise-target sample pairs (blue to orange) and linearly interpolate them at point $(c)$. In Reflow, Rectified Flow is applied again from $(c)$ to $(c)$ to straighten the flows. This procedure is repeated recursively. (B) Since iterative training on self-generated data can cause MC, we can incorporate real data (shown in red) during training to prevent collapse. (C) However, adding real data introduces additional bends to the Rectified Flow because the pairs of real data and initial Gaussian samples are not pre-paired. Our method employs reverse sampling generated real-noise pairs (red to blue) to avoid MC while simultaneously straightening the flow.
• Figure 3: Reflow Process of the DAE on a 4-D Gaussian Distribution. The figure visualizes a slice of the distribution along dimensions 0 and 1. Both kernel density estimation plots and sample points are shown for the initial and target distributions.
• Figure 4: Reflow experiment with DAE on 4D Gaussian.
• Figure 5: Comparison of Reflow and RA Reflow. Comparison of different methods. We set $\lambda = 0.5, \alpha = 8$, and use a half-scale U-Net for the experiment. Full samples for Reflow processing are provided in Appendix \ref{['fig: 8-Reflow cifar10']}.

Theorems & Definitions (13)

• Definition 4.1: Self-consuming training loops for DAE
• Theorem 4.2
• Remark 4.3: Connection to Diffusion Models
• Proposition 4.4
• Proposition 4.5
• proof : Proof of \ref{['prop: DAE collapse']}
• Lemma 1.1
• proof
• Proposition 1.2
• proof