Distilling semantic meaning from raw image data remains a challenge in machine learning. Current self-supervised paradigms face a trade-off: joint-embedding architectures produce relevant features by aggressively discarding intra-class variance, irreversibly spatial and reconstruction. Conversely, generative models preserve spatial details but struggle to isolate semantics, as their optimization is dominated by pixel variations. To bridge this divide, we propose composite subspace flow matching (CSFM). Rather than corrupting data with unstructured isotropic noise, CSFM formulates representation learning as the variance-minimizing inversion of a deterministic degradation curriculum across spectral, color, and illumination subspaces. By bounding trajectory variance with hard temporal style truncation, a capacity-constrained encoder is driven to ignore transient style artifacts and encode persistent content. Empirical evaluations across CIFAR-10, CIFAR-100, and STL-10 show that CSFM yields competitive discriminative transferability while preserving generative synthesis across both convolutional and vision transformer architectures. By avoiding the collapse pathologies of non-generative methods, CSFM forms a smooth latent space that outperforms standard optimal transport flows on linear probing and few-shot classification, while enabling coherent synthesis and trajectory interpolation. These results confirm that steering the physical dynamics of generative flows offers a scalable paradigm for learning representations that are simultaneously linearly separable and generatively invertible.
Figures & tables
Paradigm
Model
Linear Probe Accuracy
k -NN
Silhouette
100%
10%
1%
Pixel Recon.
Autoencoder (AE)
58.07%
51.08%
37.45%
48.37%
-0.0780
CDAE (CSFM Path)
57.27%
50.68%
36.06%
48.81%
-0.0599
Flow Matching
OT-Flow
67.11%
62.25%
45.75%
52.97%
-0.0454
CSFM ( t1=1.0 , No Trunc.)
69.59%
63.33%
46.31%
64.14%
-0.0098
CSFM ( t1=0.5 , Trunc.)
75.29%
71.94%
58.93%
68.34%
-0.0154
Table 1: Representation benchmark on CIFAR-10 across generative and discriminative paradigms (40K steps, baseline 20.81M tier: WRN-28-4 encoder paired with 14.83M U-Net). Best generative result in bold.
Figure 1: Topological manifold analysis via t-SNE embeddings on CIFAR-10 test set. ( Left ) OT-Flow forms dispersed, overlapping representations. ( Middle ) Truncated CSFM ( t1=0.5 ) isolates distinct semantic clusters while preserving global manifold connectivity. ( Right ) LeJEPA shatters representations into isolated topological islands.
Model
Steps
Linear (100%)
1% Few-Shot
k -NN
Silhouette
CSFM ( t1=0.5 )
40K
77.31%
63.74%
72.08%
0.0068
80K
78.59%
63.72%
71.77%
-0.0038
120K
78.51%
63.45%
70.73%
-0.0166
CSFM ( t1=1.0 )
40K
69.86%
48.16%
64.54%
-0.0099
80K
72.19%
49.01%
66.09%
-0.0114
120K
73.59%
49.34%
66.74%
-0.0154
Table 2: Decoder capacity scaling on CIFAR-10 with a fixed WideResNet-28-4 encoder (5.98M parameters) paired with the high-capacity U-Net regressor (59.10M parameters).
Configuration
Linear Probe
1% Few-Shot
k -NN
Silhouette
Asymmetric Routing Cutoff ( t0 ) with t1=1.0
t0=0.0 (No Routing)
69.09%
46.41%
63.13%
-0.0185
t0=0.001
69.12%
46.00%
63.04%
-0.0202
t0=0.025
69.22%
47.84%
64.23%
-0.0126
t0=0.050
69.52%
47.41%
64.38%
-0.0105
Style Truncation Horizon ( t1 ) with t0=0.05
Table 3: Ablation of temporal boundaries on CIFAR-10 (20.81M baseline tier, 40K steps).
Benchmark Axis
Dataset
Model Backbone
Steps
Linear Probe
1% Few-Shot
k -NN ( k=20 )
Semantic Cardinality
CIFAR-100
OT-Flow (CNN)
40K
42.27%
10.66%
33.63%
CIFAR-100
CSFM (CNN)
40K
51.58%
17.65%
38.97%
Architectural Bias
CIFAR-10
OT-Flow (ViT/DiT)
40K
51.84%
39.15%
56.81%
CIFAR-10
OT-Flow (ViT/DiT)
80K
53.27%
41.06%
58.36%
CIFAR-10
CSFM (ViT/DiT)
40K
53.30%
42.27%
55.14%
CIFAR-10
CSFM (ViT/DiT)
80K
61.49%
49.69%
62.77%
Table 4: Scalability benchmarks across semantic cardinality (CIFAR-100), backbones (CNN vs. ViT/DiT), and spatial resolution (STL-10). Evaluated under strict parameter parity within each tier. Best results per tier in bold.
Appendix figures & tables10 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 6
Parameter
Value
Operator Decay Rates
Illumination ( killum )
3.250
Color ( kcolor )
2.925
Frequency ( kfreq )
2.632
Curriculum Horizons and Projectors
Style Truncation Boundary ( t1 )
0.50
Appendix
Table 5: CSFM degradation curriculum and optimization hyperparameters.
Model
Learning Paradigm
Primary Task Objective ( Ltask )
AE
Unconstrained Reconstruction
Ex0[x0−vθ(0,0,z)22]
CDAE
Single-Step Denoising
Et,x0,x1[x0−x^θ(xt,t,z)22]
OT-Flow
Continuous Linear Flow
Et,x0,x1[vθ(xt,t,z)−(x1−x0)22]
LeJEPA
Joint Embedding
Ex0,v1,v2[21zv1−zv222]
Appendix
Table 6: Primary task objectives ( Ltask ) for comparative baselines. We denote x1∼N(0,ID) as the spatial prior and v1,v2 as independent stochastic views.
Regularization ( λreg )
Linear Probing Accuracy
k -NN ( k=20 )
Silhouette Score
100% Data
10% Data
1% Data
1×10−3
18.62%
18.12%
17.85%
31.13%
-0.1763
5×10−3
65.18%
59.81%
54.57%
64.41%
-0.0535
7.5×10−3
71.31%
68.28%
64.21%
70.31%
0.1019
1×10−2
72.97%
70.26%
66.69%
71.64%
0.1604
3×10−2
72.49%
71.02%
67.76%
71.65%
0.1738
Appendix
Table 7: Ablation of SIGReg regularization strength ( λreg ) on the LeJEPA baseline.
Figure 2: Dimensional collapse analysis via singular value decomposition (SVD) on frozen CIFAR-10 test embeddings. ( a ) Normalized singular value spectrum. ( b ) Cumulative explained variance highlighting the 90% energy threshold ( d90% ).
Figure 3: Empirical Pearson correlation matrices of the latent bottleneck dimensions on CIFAR-10 test embeddings across OT-Flow ( Left ), truncated CSFM ( t1=0.5 , Middle ), and LeJEPA ( Right ).
Model
λreg
Linear Probe
1% Few-Shot
k -NN ( k=20 )
Silhouette
CSFM
0.0 (Unregularized)
68.98%
45.50%
64.08%
-0.0077
1×10−3
69.09%
46.41%
63.13%
-0.0185
5×10−3
68.09%
46.40%
53.85%
-0.0485
1×10−2
68.44%
46.31%
53.20%
-0.0221
1×10−1
64.61%
44.96%
55.73%
0.0001
OT-Flow
0.0 (Unregularized)
66.40%
43.61%
60.40%
-0.0205
Appendix
Table 8: Ablation over structural regularization weight λreg on the 20.81M baseline tier (40K steps). CSFM evaluated with κ=6.0,β=0.7,t0=0.0,t1=1.0 .
Hyperparameter
Linear Probe
1% Few-Shot
k -NN
Silhouette
Optimal Truncation ( t1=0.5 )
Base Style Decay Rate ( κ ) with β=0.7
κ=10−4
75.53%
60.12%
66.33%
0.0062
κ=0.01
74.80%
58.46%
64.47%
0.0011
κ=0.5
75.25%
58.72%
65.60%
-0.0047
κ=3.25
76.10%
58.57%
67.27%
-0.0169
Appendix
Table 9: Ablation of continuous trajectory decay parameters ( κ and β ) on CIFAR-10 (20.81M tier, 40K steps).
Model Configuration
Uncond. FID1k ( ↓ )
Cond. FID1k ( ↓ )
ODE Error ( N=50 )
ODE Error ( N=10 )
OT-Flow
93.57
119.04
0.00015
0.00327
CSFM ( t1=1.0 )
125.97
48.84
0.00505
0.08340
CSFM ( t1=0.5 )
95.76
87.88
0.00277
0.04393
Appendix
Table 10: Generative synthesis fidelity ( FID1k ) and conditional ODE integration error (MSE vs. N=1000 baseline) at 120K steps on the high-capacity tier (65.08M total). Best results in bold.
Figure 4: Spherical linear interpolation ( λ∈[0,1] , green) and extrapolation ( λ∈/[0,1] , red) across test-set latent anchors evaluated at 120K steps. Truncated CSFM ( t1=0.5 ) demonstrates fluid semantic morphing across intermediate coordinates and maintains structural integrity into the extrapolation regime.
Learning representations that separate content and style is crucial for controllable generation and compositional generalization. However, diffusion and flow-based models trained primarily with generative objectives often produce entangled or misaligned factors. To address this gap, we introduce Contrastive Augmented Flow Matching (CAtFM), a framework that integrates contrastive regularization into an invertible flow matching formulation to promote structured content-style representations. Rather than constraining intermediate latents or velocity fields, we apply contrastive supervision to predicted endpoints during training, enforcing semantic consistency across transported distributions while allowing disentanglement to emerge implicitly, without assuming strictly pure or fully factorized content and style representations. Our main experiments operate in the CLIP embedding space, with additional validation using frozen DINO and ALIGN encoders. Across synthetic data, in-domain styles, and real-world benchmarks (ImageNet, WikiArt, DomainNet, and DTD), CAtFM improves content and style retrieval, enhances embedding cluster separation, and achieves stronger open-set robustness compared to generative and discriminative baselines. Overall, CAtFM provides a simple way to couple discriminative constraints with deterministic transport, improving disentanglement and robustness under distribution shift.
Yusong Li, Pingchuan Ma, Ming Gui +2
Computer Vision & Learning Group at the University of Munich
Strong semantic representations improve the convergence and generation quality of diffusion and flow models. Existing approaches largely rely on external models, which require separate training, operate on misaligned objectives, and exhibit unexpected scaling behavior. We argue that this dependence arises from the model's training objective, which poses a denoising task with little incentive to learn semantic representations. We introduce Self-Flow: a self-supervised flow matching paradigm that integrates representation learning within the generative framework. Our key mechanism, Dual-Timestep Scheduling, applies heterogeneous noise levels across tokens, creating an information asymmetry that forces the model to infer missing information from corrupted inputs. This drives learning strong representations alongside generative capabilities without external supervision. Our method generalizes across modalities and enables multi-modal training while following expected scaling laws, achieving superior image, video, and audio generation.
Pixel-space generative models bypass lossy latent compression, yet necessitate joint learning of global structure and fine-grained details in a high-dimensional space. Standard flow matching interpolates noise toward a fixed clean-image endpoint, leaving the spectral evolution to be learned implicitly. In this paper, we introduce Energy-Guided Flow Matching(EG-FM) that explicitly models a coarse-to-fine generative trajectory by moving endpoint. Specifically, EG-FM replaces the fixed endpoint with a heat-kernel-filtered endpoint that evolves smoothly from low-frequency image to clean image. The fraction of high-frequency signal in moving endpoint is released by an image-specific energy-guided scheduling, leading to the re-targeting of velocity in flow matching. Our framework requires no adaptation of the backbone and training data, bringing negligible cost on the training and inference stages. In our experiment, EG-FM consistently achieves lower FID on the ImageNet class-conditional image generation task at 256×256 with fewer epochs, reaching an FID of 1.55 at 200 epochs and 1.45 at 600 epochs. We continue training the generation task on the setting of 512×512 resolution, yielding a FID of 1.58 after only 40 high-resolution adaptation epochs. Furthermore, we transfer EG-FM on text-to-image generation and achieve 0.85 on GenEval score and 83.9 on DPG-Bench. Code is available at https://github.com/ysng123/EG-FM.
Haoyang Tong, Yu He, Fang Li +6
MAIS & NLPR, CASIA · JD.com · Xi'an Jiaotong University +1