Self-Improving Diffusion Models (SIMS)

• The paper introduces a negative guidance approach that combines score functions from real and synthetic data to counteract model autophagy disorder.
• It achieves state-of-the-art FID improvements on benchmarks like CIFAR-10 and ImageNet-64 while maintaining stability over up to 100 synthetic generations.
• The method offers precise distribution control, enabling fairness interventions and dynamic demographic adjustments in generated outputs.

Self-Improving Diffusion Models with Synthetic Data (SIMS) refer to a class of generative modeling techniques designed to overcome the detrimental feedback loops and distributional drift that occur when diffusion models are recursively trained on their own synthetic data. The SIMS paradigm specifically addresses challenges such as Model Autophagy Disorder (MAD) and model collapse through an explicit mechanism that treats real and synthetic data with distinct roles during training. By leveraging negative guidance, SIMS enables iterative, data-efficient self-improvement and grants fine-grained control over the generative distribution, including targeting specific demographic or fairness constraints.

1. Motivation: Autophagy Risk and Synthetic Data Loops

Diffusion models are increasingly trained with synthetic data as the availability of large, diverse real datasets becomes a bottleneck for scaling generative AI. Conventional iterative training on synthetic data, especially when drawn from prior generations of models, frequently leads to compounding approximation errors. This phenomenon, known as Model Autophagy Disorder (MAD), manifests in loss of distributional fidelity, collapse of sample diversity, and exacerbation of demographic bias. Standard recommendations have been to avoid self-consuming synthetic data loops, but they sacrifice scalability and adaptability. SIMS provides a principled framework to avoid MAD, enabling productive self-training on synthetic data while maintaining or improving generative performance (Alemohammad et al., 29 Aug 2024).

2. Formal SIMS Training Algorithm

SIMS decomposes training into three distinct phases, designed to set up and maintain a negative feedback loop:

1. Baseline Model Training: Let $\mathcal{D}$ be the real dataset. Train a base diffusion model with parameters $\theta_r$ to learn the score function $s_{\theta_r}(x_t, t)$:

   $$s_{\theta_r}(x_t, t) \sim \text{Diffusion Objective (score matching) on } \mathcal{D}$$

2. Synthetic Data Generation: Sample a synthetic dataset $\mathcal{D}_s$ from the base model.
3. Auxiliary Model Training (Synthetic Data): Fine-tune a copy of the base diffusion model (parameters $\theta_s$) exclusively on $\mathcal{D}_s$ to produce the synthetic-trained score function $s_{\theta_s}(x_t, t)$.
4. Negative Guidance for Self-improvement: During sampling/generation, synthesize new data using the extrapolated SIMS score function:

   $$s_{\theta}(x_t, t) = s_{\theta_r}(x_t, t) - \omega (s_{\theta_s}(x_t, t) - s_{\theta_r}(x_t, t)) = (1 + \omega) s_{\theta_r}(x_t, t) - \omega s_{\theta_s}(x_t, t)$$

   where $\omega > 0$ is a hyperparameter controlling the strength of negative guidance away from the synthetic data manifold.

The process can be iteratively repeated for multiple generations, since the negative guidance actively resists distributional collapse.

3. Mechanism and Theoretical Justification

Negative guidance leverages the difference in score functions ($s_{\theta_s} - s_{\theta_r}$) to quantify the distributional drift induced by exclusive synthetic-data training. By explicitly subtracting this direction during sampling, subsequent generations are "steered away" from degenerate synthetic artifacts and back toward the real data manifold. This prevents the autophagous collapse characteristic of naïve recursive training. Practically, this mechanism is robust even when the proportion of synthetic data is high (up to 60% for CIFAR-10).

Interpretation: SIMS actively "undoes" the deviation caused by synthetic training, imposing a corrective force that stabilizes distributional fidelity and augments diversity across generations.

4. Empirical Results: Robustness, Quality, and State-of-the-Art Performance

SIMS has been evaluated extensively on image generation benchmarks:

Dataset	Baseline (FID)	SIMS (FID)	Relative FID Improvement
CIFAR-10	EDM-VP (1.97)	1.33	32.5%
FFHQ-64	EDM-VP (2.39)	1.04	56.9%
ImageNet-64	EDM2-S (1.58)	0.92	41.8%
ImageNet-512	EDM2-S (2.56)	1.73	32.4%

• SIMS achieves new state-of-the-art results in FID for CIFAR-10 and ImageNet-64.
• Sample diversity and realism are visibly improved over baseline autophagous models.
• Stability is maintained in recursive synthetic augmentation for up to 100 generations.
• Collapse is completely prevented under proper $\omega$ tuning up to dataset-specific synthetic ratios.

5. Fairness and Distribution Control via SIMS

An important property of SIMS is the capacity to dynamically adjust the output distribution. For instance, on FFHQ-64 (faces), the proportion of female faces can be increased to a target ratio (e.g., from 50% to 70%) by adjusting the auxiliary model and $\omega$ accordingly, without sacrificing sample quality (FID scores either improve or remain stable for both majority and minority subgroups).

This approach is particularly valuable for fairness and bias mitigation: it provides direct control over demographic proportions or attribute frequencies within generated data, mapping the output to any desired in-domain target distribution.

6. Algorithmic Summary and Implementation

SIMS is implemented via score function extrapolation at generation time, interpolating between the base (real-trained) and auxiliary (synthetic-trained) score functions. Standard diffusion sampling pipelines can be adapted as:

• Train a base model on real data.
• Generate synthetic samples; fine-tune an auxiliary model on these.
• At inference, use the SIMS score formula (above) for each sampling step.

No modification to fundamental diffusion mechanisms is required; the negative guidance can be implemented as a weighted combination of score functions.

7. Limitations, Extensibility, and Future Directions

• Synthetic Data Ratio Threshold: Full MAD prevention is guaranteed when the training dataset contains less than a critical fraction of synthetic data (e.g., ~60% for CIFAR-10). Beyond this, mitigation rather than elimination of collapse is possible.
• Generality: While the current paradigm focuses on score-based diffusion models and image generation, a plausible implication is that negative guidance extrapolation could generalize to other generative model families and modalities.
• Distributional Control: SIMS is not limited to binary attribute alignment but is applicable for fine-grained multi-group repartitioning and complex fairness interventions.
• Further research: Extending negative guidance principles to joint multimodal setups, sequential synthetic-real feedback loops, or models with more complex attribute structures is a natural trajectory for continued paper.

8. Key Contributions Table

Contribution	Mechanism	Impact
Self-improvement	Negative guidance loop	SOTA generative quality; stable recursion
MAD prevention	Score function extrapolation	Robustness against model collapse
Distribution control	Adjustable $\omega$ and aux model	Dynamic fairness and target alignment

9. Conclusion

Self-Improving Diffusion Models with Synthetic Data (SIMS) provide a rigorously justified framework for safe, efficient, and controllable recursive training on synthetic data. Through explicit differentiation between real and synthetic data in the training pipeline, and by leveraging negative guidance, SIMS avoids model collapse, enhances generative sample quality, and enables distribution-level interventions, marking a major advance in scalable, self-evolving generative modeling (Alemohammad et al., 29 Aug 2024).