DDIM from DDPM

Reproduction of DDPM (Ho et al. 2020, NeurIPS 2020) and DDIM (Song et al. 2020, ICLR 2021) from pretrained DDPM weights.

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Setup

We recommend using uv for a faster setup.

Linux / macOS

uv venv
source .venv/bin/activate
uv pip install -r requirements.txt
uv pip install -e .

Windows

uv venv
.venv\Scripts\activate
uv pip install -r requirements.txt
uv pip install -e .

Tested with Python 3.10+, PyTorch 2.1+, CUDA 13.0.

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Reproducing results

Each notebook can be executed end-to-end:

# Notebook 1: sanity checks, noise schedule, DDIM vs DDPM at fixed seed
jupyter nbconvert --to notebook --execute notebooks/01_foundations.ipynb

# Notebook 2: η × NFE sweep, FID table, Pareto plots (LONG TO RUN!! check parameters in configs)
jupyter nbconvert --to notebook --execute notebooks/02_eta_nfe_sweep.ipynb

# Notebook 3: DDIM inversion, PSNR curve, SLERP/LERP interpolation
jupyter nbconvert --to notebook --execute notebooks/03_inversion_and_interpolation.ipynb

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Results

Notebook 1: Foundations and Sanity Checks

• Equivalence: We verify that our implemented DDIM with $\eta = 1$ exactly corresponds to DiffusersDDPM.
• Determinism: By starting from the same latent $x_T$ and sampling with different seeds, we demonstrate that DDPM yields varying outputs, whereas DDIM ($\eta = 0$) returns the same result (a deterministic process).
• Sample Quality: Generating samples from the LSUN Church dataset at NFE = 10 highlights the stark visual differences between DDPM ($\eta = 1$) and DDIM ($\eta = 0$).
• Reconstruction: We take a photograph of a famous physicist (Peter Higgs), add noise, and attempt to reconstruct it using a CelebA-HQ model with both DDIM ($\eta = 1$) and DDPM ($\eta = 1$).

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Notebook 2: $\eta \times$ NFE Sweep & FID on CIFAR-10

The following results were obtained using 3072 samples (configurable via configs/cifar10.yaml: sampling.num_samples_fid).

FID Results (3.1k Samples): DDIM vs. DDPM

(For reference, see Song et al. 2020, Table 1, 50K samples)

Key Observations:

• Low NFE Regime (10–20): $\eta=0$ (DDIM) strictly dominates. At NFE=10, $\eta=0$ achieves an FID $\approx$ 20-24, while $\eta=1$ (DDPM) yields an FID $\approx$ 47-52 (roughly 2× worse). Deterministic sampling is significantly more efficient here.
• Note on FID Deviation: Because we evaluate on ~3.1K samples instead of the 50K used in the reference paper, our absolute FID scores are systematically higher due to sample-size bias. However, statistical evaluation (Spearman rank correlation) confirms that the performance dynamics across NFE and $\eta$ closely match the original paper.

Performance and Pareto Efficiency

Hardware Note: For $\eta = 1$ and NFE = 10, we recorded an unusually high execution time. This anomaly is likely due to hardware thermal throttling during that specific run.

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Notebook 3: Inversion and Interpolation

DDIM Inversion

DDIM inversion exploits the fact that the deterministic ($\eta=0$) sampling process is invertible. We can run the DDIM forward (noise-adding) direction using the learned model $\epsilon_\theta$ to obtain a latent $x_T$, such that running DDIM sampling backward from $x_T$ successfully reconstructs $x_0$.

The forward DDIM step (Song et al. 2020, implicit Eq. 12 reversed, $\eta=0$) is defined as:

$$x_t = \sqrt{\frac{\alpha_t}{\alpha_{t-1}}} \cdot x_{t-1} + \sqrt{1 - \alpha_t} \cdot \left( 1 - \sqrt{ \frac{\alpha_t}{\alpha_{t-1}} \cdot \frac{1-\alpha_{t-1}}{1-\alpha_t} } \right) \cdot \epsilon_\theta(x_{t-1}, t-1)$$

Equivalently, this acts as an explicit Euler method on the probability-flow ODE in the forward (increasing $t$) direction. The approximation inherently improves with more steps. Below is the inversion of 4 real CIFAR-10 training images to $x_T$, followed by their resampling:

SLERP Interpolation (LSUN Bedroom 256×256)

By sampling two latents $z_1, z_2 \sim \mathcal{N}(0,I)$ and interpolating between them via Spherical Linear Interpolation (SLERP), we reproduce Fig. 8 of Song et al. 2020. The semantic content transitions smoothly because the DDIM ($\eta=0$) process acts as a continuous, invertible mapping.

SLERP Formula:

$$\text{slerp}(z_1, z_2, \alpha) = \frac{\sin((1-\alpha)\theta)}{\sin(\theta)} \cdot z_1 + \frac{\sin(\alpha\theta)}{\sin(\theta)} \cdot z_2$$

Notes on FID computation

We use clean-fid with mode="legacy_pytorch", not mode="clean".

Why legacy_pytorch? The DDIM and DDPM papers compute FID using a PyTorch implementation with bilinear resizing. clean-fid in legacy_pytorch mode reproduces this exact resize kernel, making our numbers directly comparable to Song et al. 2020 Table 1.

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Checkpoint provenance

All models use a linear β schedule (β_start=1e-4, β_end=0.02, T=1000) and predict ε (noise).

CIFAR-10: The original Ho et al. 2020 EMA checkpoint converted to diffusers format by VainF. It is downloaded automatically on first use.

Checkpoint format and the subfolder parameter

diffusers stores models in two layouts, which affect how they are loaded:

Standalone model format — used by the Google checkpoints

Pipeline format — used by the VainF CIFAR-10 checkpoint

src/models.py handles both cases automatically; callers never need to specify a subfolder.

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References

1. Ho et al. 2020 — "Denoising Diffusion Probabilistic Models", NeurIPS 2020. https://arxiv.org/abs/2006.11239

2. Song et al. 2020 — "Denoising Diffusion Implicit Models", ICLR 2021. https://arxiv.org/abs/2010.02502

3. Song et al. 2021 — "Score-Based Generative Modeling through Stochastic Differential Equations", ICLR 2021. https://arxiv.org/abs/2011.13456