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INRFlow: Flow Matching for INRs in Ambient Space
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Proposes INRFlow, a domain-agnostic flow matching transformer that trains directly in ambient data space with a conditionally independent point-wise objective, evaluated on images, 3D point clouds, and protein structures.
Problem
Flow matching generative models typically need a domain-specific two-stage pipeline (a data compressor plus latent generative model), which hinders unifying generative modeling across data modalities.
Approach
Learn flow matching directly in ambient coordinate-value space using a conditionally independent point-wise velocity objective: a PerceiverIO-style encoder produces spatially-aware latents from context coordinate-value pairs, and a decoder predicts the velocity for each coordinate independently, enabling continuous, resolution-agnostic evaluation.
Key results
- INRFlow-XL achieves FID 3.74 on ImageNet-256 (cfg=1.5) and 2.73 on ImageNet-128, competitive with latent-space DiT-XL (2.27) and SiT-XL (2.06) though with a domain-agnostic architecture.
- On Objaverse image-to-3D, INRFlow reaches ULIP-I 0.2976 and P-FID 0.3638, outperforming CLAY (0.2066 / 0.9946).
- On protein folding, INRFlow achieves C-alpha LDDT 0.722 and TM-score 0.664 versus Boltz-1's 0.923 and 0.812.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use INRFlow-L instead of StyleGAN2 | FFHQ-256 image generation · FFHQ-256 | FID-CLIP: 2.35 -> 2.18 | Helped |
| Use INRFlow-L instead of StyleGAN2 | Church-256 image generation · Church-256 | FID-CLIP: 6.21 -> 5.51 | Helped |
| Use INRFlow-XL instead of PolyINR | ImageNet-128 image generation · ImageNet-128 | FID: 2.08 -> 2.73 | Hurt |
| Use INRFlow-XL instead of PolyINR | ImageNet-128 image generation · ImageNet-128 | IS: 179.0 -> 187.6 | Helped |
| Use INRFlow-XL instead of SiT-XL | ImageNet-256 image generation · ImageNet-256 | FID: 2.06 -> 3.74 | Hurt |
| Use INRFlow instead of CLAY | Image-conditioned point-cloud generation · Objaverse | ULIP-I: 0.2066 -> 0.2976 | Helped |
| Generate at 512x512 directly instead of using bilinear interpolation | INRFlow trained on FFHQ-256 · FFHQ-256 to 512x512 | FID: 35.05 -> 23.09 | Helped |
| Generate at 512x512 directly instead of using bicubic interpolation | INRFlow trained on FFHQ-256 · FFHQ-256 to 512x512 | FID: 24.34 -> 23.09 | Helped |
| Use INRFlow instead of Boltz1 | Protein folding · AFDB-SwissProt test | Cα-LDDT: 0.923 -> 0.722 | Hurt |
| Replace grid pseudo-coordinates with randomly sampled pseudo-coordinates (ablation) | INRFlow on LSUN-Church-256 · LSUN-Church-256 | FID-CLIP: 7.32 -> 11.66 | Hurt |
| Replace grid pseudo-coordinates with KMeans++ initialization (ablation) | INRFlow on LSUN-Church-256 · LSUN-Church-256 | FID-CLIP: 7.32 -> 10.42 | Hurt |
| Use random pseudo-coordinates and increase the number of latents to 2048 (ablation) | INRFlow on LSUN-Church-256 · LSUN-Church-256 | FID-CLIP: 11.66 -> 8.95 | Helped |
Surprising findings
- Resolution-agnostic sampling works: INRFlow trained on ImageNet-256 can generate up to 2k resolution images, and a 512x512 FID of 23.09 beats bilinear (35.05) and bicubic (24.34) upsampling on FFHQ.
Limitations
- Performance lags latent-space models (DiT-XL, SiT-XL) on ImageNet-256, which use pretrained VAEs trained on much larger data.
- Protein folding results are far below Boltz-1 and hyperparameters were not optimized.
- Models are trained separately per data domain; multi-domain co-training is left to future work.
Experimental setup
Datasets: ImageNet FFHQ LSUN-Church Objaverse ShapeNet SwissProt AlphaFold Database
Benchmarks: FFHQ-256 LSUN-Church-256 ImageNet 128x128 ImageNet 256x256 Objaverse ShapeNet SwissProt
Metrics: FID FID_CLIP IS precision recall ULIP-I P-FID MMD COV 1-NNA
Baselines: DiT-XL SiT-XL ADM RIN HDiT PolyINR GEM GASP ∞-Diff CLAY LION Boltz-1
Builds on: flow matching PerceiverIO rectified flow DiT
Closest papers by meaning
- Blockwise Flow Matching: Improving Flow Matching Models For Efficient High-Quality Generation (NeurIPS 2025 · similarity 0.87)
- Improving Flow Matching by Aligning Flow Divergence (ICML 2025 · similarity 0.86)
- Metric Flow Matching for Smooth Interpolations on the Data Manifold (NeurIPS 2024 · similarity 0.86)
- Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modeling (NeurIPS 2025 · similarity 0.86)
- Path-Guided Flow Matching for Dataset Distillation (NeurIPS 2026 · similarity 0.86)
- Diff2Flow: Training Flow Matching Models via Diffusion Model Alignment (CVPR 2025 · similarity 0.86)
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