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Inverse Flow and Consistency Models
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Introduces Inverse Flow (IF), with Inverse Flow Matching and Inverse Consistency Models, to learn denoising mappings from noisy data alone by replacing unobserved clean data with generated samples inside continuous-time generative training.
Problem
Denoising and inverse generation when only noisy observations and a known noise model are available, with no ground-truth clean data.
Approach
Replace the unobserved clean data in conditional flow matching and consistency training with samples generated by the model itself (inverse ODE from noisy x1), and generalize consistency training to arbitrary forward conditional flows so that a simulation-free inverse consistency objective can be derived.
Key results
- On BSDS500 with correlated noise, ICM reaches 27.64 dB PSNR versus 27.10 for supervised and 26.32 for Noise2Void, and Noise2Self only 21.03.
- On BSDS500 with Gaussian noise, ICM reaches 28.16 dB versus 28.00 for the supervised baseline and 27.79 for Noise2Self.
- On single-cell RNA-seq, ICM raises nearest-neighbor cell type accuracy on the adult mouse brain dataset from 0.513 to 0.571 and on the mouse brain development dataset from 0.647 to 0.736.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ICM instead of the supervised method | Denoising · Gaussian noise, BSDS500 | PSNR (dB): 28.00 -> 28.16 | Helped |
| Use ICM instead of the supervised method | Denoising · Gaussian noise, Kodak | PSNR (dB): 28.91 -> 29.08 | Helped |
| Use ICM instead of the supervised method | Denoising · Gaussian noise, Set12 | PSNR (dB): 28.99 -> 29.19 | Helped |
| Use ICM instead of the supervised method | Denoising · Correlated noise, BSDS500 | PSNR (dB): 27.10 -> 27.64 | Helped |
| Use ICM instead of the supervised method | Denoising · Correlated noise, Kodak | PSNR (dB): 27.97 -> 28.53 | Helped |
| Use ICM instead of the supervised method | Denoising · Correlated noise, Set12 | PSNR (dB): 27.88 -> 28.46 | Helped |
| Use ICM instead of the supervised method | Denoising · SDE (Jacobi process), BSDS500 | PSNR (dB): 24.34 -> 24.28 | Hurt |
| Use ICM instead of the supervised method | Denoising · SDE (Jacobi process), Kodak | PSNR (dB): 25.34 -> 25.07 | Hurt |
| Use ICM instead of the supervised method | Denoising · SDE (Jacobi process), Set12 | PSNR (dB): 25.01 -> 24.74 | Hurt |
| Apply ICM denoising | Adult mouse brain single-cell RNA-seq · Adult mouse brain single-cell RNA-seq | Cell type prediction accuracy: 0.513±0.003 -> 0.571±0.003 | Helped |
| Apply ICM denoising | Mouse brain development single-cell RNA-seq · Mouse brain development single-cell RNA-seq | Cell type prediction accuracy: 0.647±0.006 -> 0.736±0.006 | Helped |
Surprising findings
- ICM outperforms the supervised model trained on clean data for Gaussian and correlated noise, which the authors attribute to supervised overfitting.
- On the Jacobi-process SDE noise, the supervised method (24.34 dB) remains better than ICM (24.28 dB) on BSDS500.
Limitations
- Requires prior knowledge of the noise distribution p(x1|x0).
- Applicability limited to transformations with one-to-one mapping; ill-posed transformations such as color-to-grayscale are excluded.
Experimental setup
Datasets: BSDS500 Kodak Set12 Fluorescence Microscopy Denoising (FMD) adult mouse brain scRNA-seq mouse brain development scRNA-seq synthetic 8-gaussians Navier-Stokes simulation
Benchmarks: BSDS500 Kodak Set12 FMD 8-gaussians Navier-Stokes
Metrics: PSNR nearest-neighbor cell type accuracy
Baselines: Supervised BM3D Noise2Void Noise2Self Inverse Flow Matching
Builds on: conditional flow matching consistency models consistency distillation Noise2Self Ambient Diffusion
Closest papers by meaning
- D-Flow: Differentiating through Flows for Controlled Generation (ICML 2024 · similarity 0.89)
- Solving Inverse Problems with FLAIR (NeurIPS 2025 · similarity 0.89)
- DEFT: Efficient Fine-tuning of Diffusion Models by Learning the Generalised $h$-transform (NeurIPS 2024 · similarity 0.88)
- EVODiff: Entropy-aware Variance Optimized Diffusion Inference (NeurIPS 2025 · similarity 0.88)
- Exact Posterior Score Estimation for Solving Linear Inverse Problems (NeurIPS 2026 · similarity 0.88)
- Consistency Posterior Sampling for Diverse Image Synthesis (CVPR 2025 · similarity 0.87)
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