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Neural Diffusion Models
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Proposes Neural Diffusion Models, which learn a time-dependent non-linear data transformation inside the forward process and train it with a simulation-free variational bound, reporting state-of-the-art likelihood on ImageNet and CelebA-HQ.
Problem
Standard diffusion models use a fixed, linear forward (noising) process, which limits flexibility and leaves a gap between the variational bound and the true negative log-likelihood.
Approach
Generalize the DDIM-style implicit forward process by applying a learnable time-dependent transformation F_phi(x,t) to data before noise injection, optimize the full variational bound simulation-free, and derive continuous-time SDE/ODE forms with JVP for exact time derivatives.
Key results
- NDM reaches 3.55 BPD on ImageNet 32 and 3.35 BPD on ImageNet 64, beating VDM (3.72, 3.40), and 2.70 BPD on CIFAR-10 versus VDM's 2.65.
- On CelebA-HQ-256, latent NDM improves LSGM's NLL bound from <=0.70 to <=0.65 with FID 7.18 vs 7.22.
- With matched architectures and 1000 steps, NDM gets 3.02 vs DDPM 3.11 NLL on CIFAR-10, but NDM's FID is slightly worse (11.82 vs 11.44).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use learnable time-dependent data transformations instead of fixed identity transformation | NDM versus DDPM · CIFAR-10, 1000 steps | NLL: 3.11 -> 3.02 | Helped |
| Use learnable time-dependent data transformations instead of fixed identity transformation | NDM versus DDPM · ImageNet 32, 1000 steps | NLL: 3.89 -> 3.79 | Helped |
| Use learnable time-dependent data transformations instead of fixed identity transformation | NDM versus DDPM · CIFAR-10, 1000 steps | FID: 11.44 -> 11.82 | Hurt |
| Use learnable time-dependent data transformations instead of fixed identity transformation | NDM versus DDPM · CIFAR-10, 10 steps | FID: 37.83 -> 31.56 | Helped |
| Train with 1000 steps and reduce sampling to 10 steps | NDM versus DDPM · CIFAR-10 | FID: 43.85 -> 48.41 | Hurt |
| Replace LSGM linear diffusion with learnable transformations | Latent NDM · CelebA-HQ-256 | FID: 7.22 -> 7.18 | Helped |
Surprising findings
- Using the simplified noise-prediction loss instead of the full objective can collapse the learned transformation to zero.
- NDM is less robust than DDPM when sampling with fewer steps than it was trained with (e.g., 1000 to 10 steps degrades FID more).
Limitations
- Learnable transformations roughly double parameter count and make training about 2.3x slower than DDPM.
- Conditional generation with classifier guidance is not directly supported when the forward process is learned.
- Less robust than DDPM to reduced sampling step counts.
Experimental setup
Datasets: MNIST CIFAR-10 ImageNet 32 ImageNet 64 CelebA-HQ-256 2D checkerboard
Benchmarks: CIFAR-10 ImageNet 32 ImageNet 64 CelebA-HQ-256 MNIST
Metrics: NLL (bits per dimension) NELBO FID
Baselines: DDPM Improved DDPM VDM Score SDE Score Flow LSGM
Builds on: DDPM DDIM Variational Diffusion Models LSGM Score SDE
Closest papers by meaning
- Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling (NeurIPS 2024 · similarity 0.93)
- Revisiting Diffusion Models: From Generative Pre-training to One-Step Generation (ICML 2025 · similarity 0.90)
- Plug-and-Play Diffusion Distillation (CVPR 2024 · similarity 0.90)
- Unified Generation, Reconstruction, and Representation: Generalized Diffusion with Adaptive Latent Encoding-Decoding (ICML 2024 · similarity 0.90)
- Learning Diffusion Models with Flexible Representation Guidance (NeurIPS 2025 · similarity 0.90)
- DisCo-Diff: Enhancing Continuous Diffusion Models with Discrete Latents (ICML 2024 · similarity 0.90)
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