Beyond Random Couplings: Contrastive Noise Alignment in Generative Flows
Lennart Wittke, Vinicius Azevedo
cs.CV, cs.LG
2026-09-16
ETH and Disney's CNA moves noise particles toward paired data with InfoNCE while staying near-Gaussian. CIFAR-10 2-step FID falls from 175.91 to 87.39, or 56.40 with OT.
Flow matching usually pairs each image with an independently sampled Gaussian. That is easy to implement and geometrically ugly: noise and data are almost uncorrelated, so the network has to learn a high-curvature transport. Minibatch OT reassigns those fixed noise samples, which straightens paths, but the noise cloud itself stays passive. It can permute points, not reshape the source.
This paper asks whether training can move the noise particles so they sit closer, in a semantic sense, to their paired data, while the batch as a whole stays close to a standard Gaussian. Inference would still draw from N(0,I).
Contrastive Noise Alignment (CNA) treats the noise batch as an interacting particle system under three forces:
The total loss is Lalign + β Lentropy + λ Lnorm. Each training step runs T=4 Adam updates on the noise (learning rate 0.02), then a standard conditional flow-matching step on the optimized pairs. Sampling is unchanged: x0 N(0,I). The theory leans on the Maxwell-Poincaré spherical CLT: low-dimensional projections of a uniform measure on a high-dimensional sphere become Gaussian. As β→∞, angular entropy drives directions toward uniformity, and those projections recover N(0,I) asymptotically.
Unconditional CIFAR-10 uses Tong et al.'s OT-CFM setup; all baselines are reproduced. Euler 2-step FID: independent coupling (I-CFM) 175.91, OT-CFM 91.75, CNA (β=2) 87.39, CNA+OT (β=2) 56.40. At 4 steps, CNA+OT scores 22.64 against OT's 30.00, about a 25% drop. At 128 steps, CNA+OT with β=5 reaches 4.06, slightly better than I-CFM's 4.37; the same method with β=2 scores 5.25, worse than independent coupling. Path curvature κ at Euler-128 falls from 0.0479 (I-CFM) to 0.0251 (CNA+OT).
On ImageNet32, CNA alone does not beat OT-CFM. CNA+OT (β=5) cuts 1-step FID from OT's 252.88 to 166.07, 2-step to 71.78, 4-step to 26.86. Higher step counts need a larger β: β=30 yields 16-step FID 8.96 versus OT's 9.41. Matched-pair cosine similarity rises from OT's 0.0379 (CIFAR) / 0.0491 (ImageNet32) to 0.0597 / 0.0707.
| Method | CIFAR Euler-2 FID | ImageNet32 Euler-1 FID |
| I-CFM | 175.91 | 419.92 |
| OT-CFM | 91.75 | 252.88 |
| CNA (β=2) | 87.39 | 250.87 |
| CNA+OT | 56.40 (β=2) | 166.07 (β=5) |
Ablations show all three forces are required. Alignment alone drops Euler-4 FID from 30.00 to 22.60, then the prior collapses and Dopri5 FID jumps from 3.66 to 10.52. Adding entropy and the norm penalty lands at Euler-4 25.24 and Dopri5 3.56. Training throughput falls by about 2%; in CNA+OT the bottleneck remains the OT init.
For few-step generation, CNA moves part of the "find a straight path" burden from the network onto the prior, at zero inference cost. It is orthogonal to methods that change the regression target, such as Shortcut and MeanFlow, so stacking is plausible. The catch is β: low β helps few-step FID, high β keeps the Gaussian and protects many-step quality. CNA without OT barely helps on ImageNet32; the practical recipe is CNA+OT.
This is an incremental change to coupling geometry, not a new generative family. All experiments stay at 32×32 unconditional pixel space.
The authors flag the core tension: the closer noise sits to data, the less Gaussian it is. Low β looks good at few steps and hurts Dopri5; high β reverses that. CNA+OT (β=2) already loses to independent coupling at CIFAR 128-step FID, so aggressive alignment taxes fully sampled quality. Noise is still initialized from random Gaussians, so the starting point can be poor. There is no conditional setup, no latent space, and no resolution above 32. Gaussianity from InfoNCE is an asymptotic statement; finite batches and finite dimension are approximations. The appendix also notes that the regularizer only proxies the angular piece of KL and ignores conditional radial entropy.