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System-Embedded Diffusion Bridge Models
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Proposes System-embedded Diffusion Bridge Models (SDB), a supervised bridge that embeds a known linear measurement system into a matrix-valued linear SDE, and evaluates it on four linear inverse problems plus misspecified MRI/CT settings.
Problem
Supervised diffusion bridges for linear inverse problems ignore the known measurement system structure, leading to redundant noise in range space and weaker generalization when the system parameters change at deployment.
Approach
Embed the measurement matrix A (via its pseudoinverse) and noise covariance into the mean and covariance of a Markovian linear SDE so that range-space and null-space components follow separate schedules; the null-space schedule reduces to an OT-ODE in the SB variant.
Key results
- SDB (SB) achieves the best FID on CelebA-HQ inpainting (4.63) and DIV2K superresolution (81.56), and the best PSNR on MRI (29.81) and CT (46.67) in the unified benchmark.
- Under MRI misspecification (lambda_1 reduced), SDB's performance gap over baseline bridges widens from lambda_1=14 onward.
- SDB (VE) reaches PSNR 32.12 and SSIM 0.944 on CelebA-HQ inpainting, the highest reconstruction scores on that task.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Embed the measurement system in the diffusion bridge (SDB (SB) instead of IR-SDE) | Diffusion bridge · Inpainting - CelebA-HQ | FID: 4.68 -> 4.63 | Helped |
| Embed the measurement system in the diffusion bridge (SDB (SB) instead of IR-SDE) | Diffusion bridge · Inpainting - CelebA-HQ | LPIPS: 0.031 -> 0.031 | No clear effect |
| Embed the measurement system in the diffusion bridge (SDB (SB) instead of IR-SDE) | Diffusion bridge · Inpainting - CelebA-HQ | PSNR: 29.92 -> 30.40 | Helped |
| Embed the measurement system in the diffusion bridge (SDB (SB) instead of IR-SDE) | Diffusion bridge · Inpainting - CelebA-HQ | SSIM: 0.912 -> 0.930 | Helped |
| Embed the measurement system in the diffusion bridge (SDB (SB) instead of I2SB) | Diffusion bridge · Superresolution - DIV2K | FID: 83.73 -> 81.56 | Helped |
| Embed the measurement system in the diffusion bridge (SDB (SB) instead of I2SB) | Diffusion bridge · Superresolution - DIV2K | LPIPS: 0.176 -> 0.226 | Hurt |
| Embed the measurement system in the diffusion bridge (SDB (SB) instead of DDBM) | Diffusion bridge · Superresolution - DIV2K | PSNR: 25.79 -> 26.10 | Helped |
| Embed the measurement system in the diffusion bridge (SDB (SB) instead of DDBM) | Diffusion bridge · Superresolution - DIV2K | SSIM: 0.720 -> 0.724 | Helped |
| Embed the measurement system in the diffusion bridge (SDB (SB) instead of IR-SDE) | Diffusion bridge · CT Reconstruction - RSNA | FID: 18.88 -> 15.02 | Helped |
| Embed the measurement system in the diffusion bridge (SDB (SB) instead of GOUB) | Diffusion bridge · CT Reconstruction - RSNA | LPIPS: 0.024 -> 0.018 | Helped |
| Embed the measurement system in the diffusion bridge (SDB (SB) instead of DDBM) | Diffusion bridge · CT Reconstruction - RSNA | PSNR: 44.415 -> 46.672 | Helped |
| Embed the measurement system in the diffusion bridge (SDB (SB) instead of GOUB) | Diffusion bridge · CT Reconstruction - RSNA | SSIM: 0.967 -> 0.982 | Helped |
Surprising findings
- Under the unified reimplementation, prior bridge methods perform within a narrow band, with PSNR on MRI spanning only about 28.6 to 29.0 dB.
Limitations
- Nonlinear measurement systems are only treated via a preliminary local linearization for differentiable systems.
- Simple linear variance schedules are used for range and null spaces; optimal scheduling is left open.
- Evaluated only in 2D; 3D CT and MRI remain future work.
Experimental setup
Datasets: CelebA-HQ DIV2K RSNA Intracranial Hemorrhage Br35H
Benchmarks: CelebA-HQ inpainting DIV2K superresolution RSNA CT reconstruction Br35H MRI reconstruction
Metrics: FID LPIPS PSNR SSIM
Baselines: I2SB IR-SDE GOUB DDBM DPS ΠGDM DDNM
Builds on: I2SB IR-SDE GOUB DDBM Denoising Diffusion Null-Space Models
Closest papers by meaning
- Stability and Generalizability in SDE Diffusion Models with Measure-Preserving Dynamics (NeurIPS 2024 · similarity 0.88)
- SBNO : Schrödinger Bridge Neural Operator for the Forward and Inverse Problems under Missing Information (NeurIPS 2026 · similarity 0.87)
- Learning Single Index Models with Diffusion Priors (ICML 2025 · similarity 0.87)
- Denoising Diffusion Bridge Models (ICLR 2024 · similarity 0.87)
- Diffusion Bridge Implicit Models (ICLR 2025 · similarity 0.87)
- Self-diffusion for Solving Inverse Problems (NeurIPS 2025 · similarity 0.87)
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