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Conditional Variational Diffusion Models
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Learns the variance schedule of a conditional variational diffusion model jointly with training (factorized, pixel-wise schedule with a regularizer) and applies it to super-resolution microscopy, quantitative phase imaging, and ImageNet super-resolution.
Problem
Diffusion models for inverse problems are sensitive to the variance schedule, which is usually hand-tuned per application at high time cost and without guaranteed optimality.
Approach
Extends variational diffusion models to the conditional case by parametrizing the schedule as gamma(t,x)=exp(-lambda(x) rho(t)) with separable learnable networks (monotonic in t, pixel-wise via x), trained with a Deep Galerkin consistency loss and a gamma'' regularizer motivated by discretization error analysis.
Key results
- On BioSR, CVDM achieves best resolution on CCP (96 nm), ER (152 nm), MT (97 nm), and F-actin (98 nm), improving resolution by 4.42% over CDDPM and 26.27% over DFCAN.
- On synthetic HCOCO QPI, CVDM reaches MS-SSIM 0.943 and MAE 0.073 versus US-TIE 0.907/0.110 and CDDPM 0.881/0.134.
- On clinical brightfield QPI, CVDM gets MS-SSIM 0.892/0.742/0.851 across three samples, consistently above US-TIE and CDDPM.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the learned schedule-curvature regularization term (ablation) | CVDM · Inverse problems | performance | Helped |
| Use a single learned schedule instead of pixel-wise schedules (ablation) | CVDM · QPI synthetic dataset | performance | Hurt |
| Factorize beta into separate time- and condition-dependent functions (ablation) | CVDM · Inverse problems | performance | Helped |
| Learn the variance schedule during training rather than fine-tuning it as a hyperparameter | CVDM versus fine-tuned CDDPM · Super-resolution microscopy | Resolution (nm): +4.42% | Helped |
Surprising findings
- The paper argues that the continuous-time diffusion loss's invariance to the schedule does not hold in practice under discretization, motivating a regularizer on the schedule's second derivative.
Limitations
- Schedule-learning gains rely on a regularization term (gamma'') whose weight alpha must be set; without it the schedule can converge to a degenerate solution.
- The QPI evaluation on clinical data uses diffusion models in a zero-shot setting from synthetic training, with ground truth derived from polynomial fitting.
- ImageNet super-resolution results are only comparable, not clearly superior, to prior methods.
Experimental setup
Datasets: BioSR HCOCO ImageNet 1K
Benchmarks: BioSR HCOCO ImageNet 1K
Metrics: MS-SSIM MAE resolution (nm) SSIM PSNR
Baselines: DFCAN CDDPM US-TIE
Builds on: Variational Diffusion Models CDDPM Deep Galerkin Method
Closest papers by meaning
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.89)
- DEFT: Efficient Fine-tuning of Diffusion Models by Learning the Generalised $h$-transform (NeurIPS 2024 · similarity 0.89)
- EVODiff: Entropy-aware Variance Optimized Diffusion Inference (NeurIPS 2025 · similarity 0.88)
- Align Your Steps: Optimizing Sampling Schedules in Diffusion Models (ICML 2024 · similarity 0.88)
- Variational Control for Guidance in Diffusion Models (ICML 2025 · similarity 0.88)
- Adaptive Non-Uniform Timestep Sampling for Accelerating Diffusion Model Training (CVPR 2025 · similarity 0.88)
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