Denoising Diffusion Probabilistic Models
NeurIPS, 2020 · paper · AI and machine learning
Presents high-quality image synthesis using diffusion probabilistic models, linking them to denoising score matching. It reports an Inception score of 9.46 and FID of 3.17 on CIFAR10, and sample quality similar to ProgressiveGAN on 256x256 LSUN.
Checked: PDF from arxiv.org, fetched 4 Oct 2026. Page numbers are those of that PDF.
1 finding
Substance Section 4.4 defines the interpolated latent as 'x̄t = (1 − λ)x0 + λx′0', a mix of the clean source images, whereas the procedure it describes (encode to xt, x′t ∼ q(xt|x0), then decode x̄0 ∼ p(x0|x̄t)) requires x̄t = (1 − λ)xt + λx′t.
- p. 8 Section 4.4 Interpolation, first sentence
x̄t = (1 − λ)x0 + λx′0
- p. 8 Section 4.4 Interpolation, first sentence
decoding the linearly interpolated latent ¯xt = (1 −λ)x0 + λx′0 into image space
Judge's note: The crop C004-b and page image p008 show subscripts 0 on both terms of the formula. In the same paragraph, xt and x′t are obtained with q as a stochastic encoder. The next sentence says 'We fixed the noise … so xt and x′t remain the same', which only matters if they enter the interpolation. Fig. 8 (left) labels mixing x0 and x′0 as 'Pixel-space interpolation', the very thing the method is set against. As printed, the formula describes a different procedure from the one the text describes.
Second check: another model agreed
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5 minor (typos and the like; most checked by the judge only)
Wording Table 4, which 'accompanies Fig. 5', labels its rows 'Reverse process time (T − t + 1)', while the x-axes of Fig. 5 are labelled 'Reverse process steps (T − t)'. The two labels differ by one, and the paper does not explain the offset.
- p. 13 Table 4 column header
Reverse process time (T − t + 1)
- p. 7 Figure 5 x-axes
Reverse process steps (T − t)
Only the authors can say what is right here.
Judge's note: Checked page images p013 (Table 4 header; rows run 1000 to 100) and p007 (the Fig. 5 axes run 0 to 1000 and are labelled T − t). The Table 4 rate at 1000 (1.77581) roughly matches the endpoint of the Fig. 5 rate curve, so the data appear consistent and only the index convention is unclear. Only the authors can say which t each row belongs to.
Second check: another model agreed
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Typo The noise predictor is written with one argument, ϵθ(xt), in the middle of Eq. (11) and in Eq. (15), but as ϵθ(xt, t) on the right-hand side of Eq. (11), in Eq. (12), in Eq. (14) and in Algorithms 1–2.
- p. 4 Eq. (11), middle expression
√1 − ᾱtϵθ(xt)
- p. 7 Eq. (15)
x̂0 = (xt − √1 − ᾱtϵθ(xt))/√ᾱt
Judge's note: Checked on page images p004 and p007. Eq. (11) has 'µ̃t(xt, 1/√ᾱt(xt − √(1−ᾱt) ϵθ(xt)))' in the middle and 'ϵθ(xt, t)' on the right. The text just below it also says 'predict ϵ from xt'. Eq. (15) has 'ϵθ(xt)'. The meaning is clear, so this is a cosmetic notation inconsistency.
Second check: none (judge only)
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Typo The last row of Table 2 labels the objective '‖ϵ̃ − ϵθ‖² (Lsimple)' with a tilde on ϵ, but Eq. (14) and Algorithm 1 define Lsimple with the plain noise ϵ; ϵ̃ is never defined.
- p. 5 Table 2, last row
∥˜ϵ −ϵθ∥2 (Lsimple)
- p. 5 Eq. (14)
Lsimple(θ) := Et,x0,ϵ
Judge's note: The crop C002-a and page image p005 show the tilde over ϵ in Table 2. Eq. (14) on the same page uses ϵ without a tilde. It is probably carried over from the ‖µ̃ − µ̃θ‖² row by analogy. The objective can still be identified, so this is cosmetic.
Second check: none (judge only)
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Typo The µ̃-prediction block of Table 2 writes '‖µ̃ − µ̃θ‖²' with a tilde on the model mean, whereas Eq. (8) writes the same comparison as ‖µ̃t − µθ‖².
- p. 5 Table 2, µ̃ prediction block, third row
∥˜µ −˜µθ∥2
Judge's note: The crop C003-a shows µ̃θ with a tilde. Eq. (1) and Eq. (8) use µθ without one. The tilde can be read as 'model estimate of µ̃', so either form could be legitimate. This is a minor notation inconsistency.
Second check: none (judge only)
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Typo Appendix D refers to 'the CelebA 256 × 256 dataset' and 'source CelebA 256 × 256 images' for the experiments in Fig. 7 and Fig. 9, which the main text and captions describe as using CelebA-HQ 256 × 256.
- p. 15 Appendix D, 'Latent structure' and 'Coarse-to-fine interpolation' paragraphs
intermediate latent for the CelebA 256 × 256 dataset
- p. 7 Figure 7 caption
CelebA-HQ 256 × 256 samples share high-level attributes
Judge's note: Page image p015 shows 'CelebA 256 × 256' in both the 'Latent structure' and 'Coarse-to-fine interpolation' paragraphs. The Fig. 7 caption on p007 says 'CelebA-HQ 256 × 256'. Section 4.4 and the Fig. 8 caption also say CelebA-HQ. From context this is shorthand, so it is cosmetic.
Second check: none (judge only)