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Understanding Hallucinations in Diffusion Models through Mode Interpolation
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Shows that diffusion models hallucinate by smoothly interpolating between nearby data modes, and that trajectory variance of predicted x0 in late reverse steps detects these hallucinations, enabling filtering that mitigates recursive-training collapse.
Problem
Diffusion models generate samples that lie entirely outside the support of the training distribution (hallucinations), such as extra fingers in hands; the mechanism behind this is unclear.
Approach
Hallucinations arise from "mode interpolation": a smooth learned score approximates the sharp discontinuous true score between nearby modes, so samples fall in gaps between modes. The variance of the predicted x0 trajectory over the final reverse steps separates hallucinated from in-support samples, and this metric can filter hallucinations during recursive training.
Key results
- Trajectory-variance metric removes over 95% of hallucinations while retaining 96% of in-support samples on synthetic datasets.
- On Hands, about 80% of hallucinated samples are eliminated while retaining about 81% of in-support samples (based on ~130 manually labeled images).
- On MNIST recursive training, variance-based filtering yields lower FID than random filtering across generations, slowing collapse.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Filter samples using trajectory variance | DDPM · Simple Shapes | hallucination rejection rate: 95% | Helped |
| Filter samples using trajectory variance | DDPM · 1D Gaussian | hallucination rejection rate: 95 % | Helped |
| Filter samples using trajectory variance | DDPM · 2D Gaussian | hallucination rejection rate: 96% | Helped |
| Filter samples using trajectory variance | ADM · Hands | hallucination rejection rate: ~80% | Helped |
| Filter recursive-training samples using trajectory variance instead of random filtering | DDPM · MNIST | FID | Helped |
| Increase the number of training samples | DDPM · 1D Gaussian | mode interpolation frequency | Helped |
| Increase the distance between Gaussian modes | DDPM · 1D Gaussian | mode interpolation frequency | Helped |
| Increase the number of sampling timesteps | DDPM · 1D Gaussian | mode interpolation frequency | Helped |
| Use the true score function instead of the learned network | Reverse diffusion sampling · Gaussian mixtures | mode interpolation | Helped |
| Filter recursively generated samples using trajectory variance instead of random filtering | DDPM · 2D Gaussian and Simple Shapes | hallucination rate across generations | Helped |
| Filter recursively generated samples using trajectory variance instead of random filtering | DDPM · MNIST | FID | Helped |
| Train a VDM instead of a DDPM | 2D Gaussian · 2D Gaussian | hallucination frequency | Helped |
Surprising findings
- Sampling with the true score function produces no mode interpolation, pointing to the learned network's smoothing as the cause.
- On the Hands dataset, the metric detects hallucinations only to a moderate degree (about 80% removal with 81% retention).
Limitations
- Metric requires choosing a timestep window that is dataset- and schedule-specific.
- Hands evaluation uses a small manually labeled set (~130 images) and detection is only moderately accurate.
- Analysis is limited to small synthetic settings and a single real-world case, so the link to large text-to-image models is a hypothesis.
Experimental setup
Datasets: 1D Gaussian mixture 2D Gaussian grid Simple Shapes Hands MNIST
Benchmarks: Simple Shapes 1D Gaussian mixture 2D Gaussian grid Hands MNIST
Metrics: hallucination removal rate in-support retention rate FID precision recall sensitivity specificity
Baselines: random filtering
Builds on: DDPM ADM Variational Diffusion Models classifier-free guidance
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