Stabilizing Self-Consuming Diffusion Models with Latent Space Filtering

Conference: AAAI2026
arXiv: 2511.12742
Authors: Zhongteng Cai, Yaxuan Wang, Yang Liu, Xueru Zhang
Code: GitHub
Area: Image Generation
Keywords: self-consuming training, model collapse, diffusion models, latent space filtering, data quality

TL;DR

This paper proposes Latent Space Filtering (LSF), a method that analyzes the degradation of low-dimensional structure in the latent representations of self-consuming diffusion models and uses confidence scores from a probing classifier to filter low-quality synthetic data. Under a fixed training budget, LSF effectively mitigates model collapse without requiring additional real data or an enlarged training set.

Background & Motivation

State of the Field

As synthetic data proliferates on the internet, new-generation generative models inevitably train on datasets containing synthetic samples, forming a "self-consuming loop." Research has shown that this loop leads to model collapse—degraded generation quality, reduced diversity, and the forgetting of rare samples.

Limitations of Prior Work

• Accumulating historical data: Storage and computation costs grow linearly (e.g., CelebA requires 582 MB by generation 5).
• Injecting fresh real data: Acquiring labeled data is costly in practice.
• Modifying the training procedure (e.g., SIMS score extrapolation, self-correction): These approaches become unstable over multiple generations or sacrifice diversity.
• Existing analyses focus on input space: The structural changes in latent representations are largely overlooked.

Core Motivation

The paper seeks to understand model collapse from a latent space perspective—examining how the low-dimensional structure of latent representations degrades across self-consuming generations—and to develop a filtering mechanism that requires no additional real data and incurs no extra training cost.

Core Problem

1. How does the low-dimensional structure of a self-consuming diffusion model's latent space evolve across training generations?
2. Can the quality of latent representations be exploited to filter low-quality synthetic data and thereby mitigate model collapse?
3. How can a theoretical quantitative connection between latent space degradation and filtering criteria be established?

Method

Latent Representation Extraction

The U-Net encoder \(e^{(0)}\) of the initial model (trained solely on real data) is used to extract latent representations. For samples \(\mathbf{x}^{(k)}\) generated at generation \(k\), the latent representation at denoising timestep \(t\) is:

\[\mathbf{h}_t^{(k)} = e^{(0)}(\mathbf{x}^{(k)}, t)\]

OLE Metric for Low-Dimensional Structure

The Orthogonal Low-rank Embedding (OLE) score measures inter-class subspace orthogonality:

\[\text{OLE}_t^{(k)} = \sum_{c \in \mathcal{C}} \|\mathbf{M}_{c,t}^{(k)}\|_* - \|\mathbf{M}_t^{(k)}\|_*\]

where \(\|\cdot\|_*\) denotes the nuclear norm. A lower OLE indicates more orthogonal subspaces and better structure.

Key Findings: (1) At a fixed timestep, OLE increases with generation index, indicating progressive degradation of latent structure. (2) At a fixed generation, OLE follows a U-shape—intermediate timesteps exhibit the best structure.

Theoretical Analysis 1: Lower Bound on OLE (Theorem 1)

Assuming two-class latent representations follow a noisy low-rank Gaussian distribution \(\mathcal{N}(\mathbf{0}, \mathbf{U}_c\mathbf{U}_c^\top + \sigma^2\mathbf{I}_d)\), when the maximum principal angle \(\tilde{\theta}\) between subspaces decreases (i.e., subspaces become more aligned), the lower bound on OLE increases:

\[\mathbb{E}[\text{OLE}(\mathbf{M}_0, \mathbf{M}_1)] \geq C_1 - C_2 \cdot \phi(\tilde{\theta})\]

where \(\phi(\tilde{\theta}) = \sqrt{2n}\sqrt{\ell\cos\tilde{\theta}} + \sqrt{2n(2n-1)}\sqrt{1-\cos\tilde{\theta}}\), which decreases as \(\theta\) decreases, causing the lower bound to increase.

Latent Space Filtering (LSF)

Mechanism: OLE is a batch-level metric and cannot filter individual samples. The method instead uses the confidence of a probing classifier as a per-sample proxy.

1. Extract latent representations from real data and train a softmax regression classifier.
2. For any sample \((\mathbf{x}, y)\), compute the confidence for the correct class:

\[\xi(\mathbf{x}, y) = \frac{\exp\{o_y(\mathbf{x})\}}{\sum_{c \in \mathcal{C}} \exp\{o_c(\mathbf{x})\}}\]

1. Select the \(N\) samples with the highest confidence from the accumulated dataset to form the training set.

Theoretical Analysis 2: Upper Bound on Confidence (Theorem 2)

The expected confidence of the Bayes-optimal classifier satisfies:

\[\xi(\theta) \leq \frac{1}{2\sigma^2(\sigma^2+1)} \varsigma(r\sin^2\theta)\]

As the subspace angle \(\theta \to 0\), the upper bound decreases, confirming that classifier confidence genuinely reflects subspace orthogonality.

Algorithm

1. Train the probing classifier on real data (required only once; 65K parameters).
2. At each generation: generate synthetic data → construct accumulated/mixed dataset → compute per-sample confidence → select top-\(N\) high-confidence samples → train the new model.

Key Experimental Results

Datasets and Setup

• MNIST (28×28, 10 classes), CIFAR-10 (32×32, 10 classes), CelebA (64×64, 4 classes)
• Fine-tune for 3 epochs with 1,000 samples per generation; generate 10,000 samples for evaluation
• Self-consuming training over 5 generations

Main Results (MNIST & CelebA)

Method	Extra Real Data	Fixed Budget	FID Trend	Precision	Recall
SYN (synthetic only)	✗	✓	Continuously worsens	Decreasing	Decreasing
SYN-ADD (30% real)	✓	✓	Partially mitigated	Moderate	Moderate
ACU (accumulation)	✗	✗	Stable	High	High
ACUR (random sampling)	✗	✓	Close to ACU	Moderate–high	High
ACUR-SIMS	✗	✓	Unstable fluctuation	Fluctuating	Fluctuating
ACUR-SC	✗	✓	Increasing	Moderate	Low
ACU-LSF (Ours)	✗	✓	Lowest / stable	Highest	Comparable to ACU

Key Advantages

• ACU-LSF achieves the lowest FID and highest Precision under a fixed budget, with Recall comparable to ACU.
• Compared to ACU: the probing classifier requires only 65K parameters and 109 MB of features (vs. 32M parameters and 582 MB of data).
• ACUR-SIMS becomes unstable due to repeated score extrapolation.
• ACUR-SC maintains acceptable Precision but suffers a significant drop in Recall, indicating reduced diversity.

Filtering Efficacy Validation

• Confidence scores for later-generation samples are systematically lower, confirming that confidence discriminates between real and synthetic samples.
• Filtered datasets contain samples from earlier generations on average, with a higher proportion of real data.
• Larger accumulated data pools yield more effective filtering.

Highlights & Insights

• Novel latent space perspective: This is the first systematic study of low-dimensional structural degradation in latent representations under self-consuming diffusion model training.
• Complete theoretical framework: Theorem 1 establishes a quantitative link between OLE and subspace orthogonality; Theorem 2 proves that classifier confidence is a valid proxy for OLE.
• High practicality: No additional real data or enlarged training sets are required, and the probing classifier incurs minimal training cost (65K parameters).
• U-shaped OLE finding: Reveals that representation quality first improves and then declines across the denoising trajectory, consistent with the unimodal trajectory of representation quality.
• Compatible with multiple training paradigms: LSF can be integrated into purely synthetic or accumulation-based self-consuming loops.

Limitations & Future Work

• Fixed class assumption: Dynamic class changes in continual learning or unlearning scenarios are not addressed.
• Dependence on the initial model: If the initial model is of poor quality, the evaluation baseline becomes unreliable.
• Validated only on DDPM: Applicability to more advanced diffusion models (Latent Diffusion, DiT) remains to be verified.
• Low-resolution experiments: The maximum resolution tested is 64×64 (CelebA); high-resolution images are not evaluated.
• Unconditional/simple conditional generation: Complex conditional generation scenarios such as text-to-image are not validated.
• Filtering may introduce selection bias: The method consistently favors samples close to the training distribution, potentially suppressing beneficial distributional exploration.

Related Work & Insights

• vs. MAD (Alemohammad et al.): MAD primarily defines the problem and provides theoretical analysis; this paper offers a concrete and actionable filtering solution.
• vs. SIMS: SIMS is effective within a single generation via score function extrapolation but becomes unstable across multiple generations; LSF remains consistently effective.
• vs. Self-Correction: SC maps synthetic samples toward real-distribution cluster centers, sacrificing diversity (low Recall); LSF preserves diversity.
• vs. Data Accumulation (ACU): ACU requires storing all historical data with linearly growing training costs; LSF achieves comparable quality under a fixed budget.
• vs. Variance Filtering (Hallucination): Variance filtering requires access to sampling trajectories, which is impractical; LSF requires only a single forward pass.

The latent space quality assessment paradigm can be generalized to self-consuming training of other generative models such as GANs and VAEs. The use of a probing classifier as a data quality proxy is applicable to large-scale data cleaning and selection. The OLE metric can serve as an online diagnostic tool for monitoring generative model degradation. The approach is highly aligned with the Data-Centric AI philosophy—optimizing data quality rather than model architecture.

Rating

• Novelty: ⭐⭐⭐⭐ — Analyzing model collapse from a latent space perspective is a genuinely new starting point with solid theoretical contributions.
• Experimental Thoroughness: ⭐⭐⭐ — Three datasets with multi-baseline comparisons, but limited by low resolution and the absence of large-scale experiments.
• Writing Quality: ⭐⭐⭐⭐ — Clear structure, tight integration of theory and experiments, and rich intuitive figures.
• Value: ⭐⭐⭐⭐ — Highly practical and addresses an important problem (a core challenge in the era of synthetic data); the method is concise and efficient.

Related Papers

• [ICML 2026] Evaluating the Representation Space of Diffusion Models via Self-Supervised Principles
• [ICLR 2026] Adapting Self-Supervised Representations as a Latent Space for Efficient Generation
• [CVPR 2026] Latent Diffusion Inversion Requires Understanding the Latent Space
• [ICML 2025] Hessian Geometry of Latent Space in Generative Models
• [CVPR 2025] Probability Density Geodesics in Image Diffusion Latent Space