We introduce the Sphere Encoder, an efficient generative framework capable of producing images in a single forward pass and competing with many-step diffusion models using fewer than five steps. Our approach works by learning an encoder that maps natural images uniformly onto a spherical latent space, and a decoder that maps random latent vectors back to the image space. Trained solely through image reconstruction losses, the model generates an image by simply decoding a random point on the sphere. Our architecture naturally supports conditional generation, and looping the encoder/decoder a few times can further enhance image quality. Across several datasets, the sphere encoder approach yields performance competitive with state of the art diffusions, but with a small fraction of the inference cost. Project page is available at https://sphere-encoder.github.io .
Figures & tables
Figure 1: Selected images generated by the Sphere Encoder in one-step for CIFAR-10 ( 32×32 ) and Animal-Faces, two-steps for Oxford-Flowers, and four-steps for ImageNet ( 256×256 ).
Figure 2: A sphere encoder E maps the natural image distribution uniformly onto a global sphere S . The decoder D then generates a realistic image by decoding a random point on the sphere.
Figure 3: Posterior hole problem in VAEs . Columns: (1) Input images; (2) Autoencoder reconstructions; (3) Samples from standard Gaussian prior; and (4) Samples from estimated Gaussian posterior on Animal-Faces training set. Unlike modern FLUX.1/2 ( Labs et al., 2025 ) and SD-VAE ( Podell et al., 2024 ) , our sphere encoder produces realistic images by decoding random points sampled from the sphere.
Figure 4: Spherifying latent with noise . Encoder E maps image x to a latent, which f projects to v on sphere S . During training, random Gaussian noise σ⋅e is added to v , where σ is jittered magnitude. Decoder D reconstructs the image x^ from the re-projected noisy latent f(v+σ⋅e) .
method
steps
rFID ↓
gFID ↓
IS ↑
conditional generation w/o cfg
sphere-l
1
0.59
18.68
9.1
2
-
8.28
9.9
4
-
2.72
10.5
6
-
1.65
10.7
stylegan 2 ( Karras et al., 2020 )
1
-
6.96
9.53
Table 1: Few-step generation results on CIFAR-10.
Figure 5: Uncurated CIFAR-10 conditional generation with different sampling steps and with/without CFG. Convincing images can be formed with a single forward pass, with reliability and gFID improving with up to 4 steps.
sphere-l model ╲ steps
1
2
4
6
of w/ cfg=1.6
25.12
14.08
11.25
10.63
of
27.12
16.60
12.98
12.26
af
21.70
19.29
18.23
17.97
stylegan 2 ( Karras et al., 2020 )
af - cat
5.13
-
-
-
af - dog
19.37
-
-
-
Table 2: Few-step generation results (gFID ↓ ) on Animal-Faces (AF) and Oxford-Flowers (OF).
Figure 6: Latent interpolation on Animal-Faces and Oxford-Flowers. Images are generated in 4 steps without CFG. (left) Interpolation in a 2D space that spans 4 synthetic images. (right) Each row interpolates between a random vector e on the sphere and a class conditional vector y . Note that our model exhibits fast/sudden transitions between image classes rather than producing “hybrid” images that unrealistically merge properties of different object types. This property is necessary for a model to reliably convert random samples from the sphere into realistic images, as it makes the probability of observing a hybrid image small.
method
params
steps
gFID ↓
IS ↑
gans
biggan-deep ( 4 )
56 M
1
6.90
171.4
stylegan-xl ( 67 )
166 M
1
2.30
265.1
gigagan ( 34 )
569 M
1
3.45
225.5
diffusions
adm-g ( 13 )
554 M
250
4.59
186.7
adm-g
554 M
25
5.44
-
sid ( 29 )
2 B
1000
2.44
256.3
Table 3: Few-step generation results on ImageNet 256×256 .
Figure 7: Latent space visualization using random projection on CIFAR-10 training set. Each sphere shows the latent vectors of a different class. The conditional latent distributions appear approximately uniform.
Figure 8: Conditional manipulation via iterative encoding and decoding on ImageNet model. We demonstrate the model’s expressivity using an out-of-domain input (a “woolly panda” top-left). Each row shows the result of conditioning the iterative process on different ImageNet classes without CFG. For example, the first row is conditioned on class 580 (greenhouse, nursery, glasshouse).
Figure 9: Image crossover using the sphere encoder trained on Animal-Faces. A composite of two images (A and B) is iteratively processed through the encoder-decoder pipeline until it converges to a coherent sample on the learned image manifold.
Figure 10: Quantitative impact of the angle α on ImageNet.
w/o cfg
w/ cfg =1.6
loss L
steps
rFID ↓
gFID ↓
IS ↑
gFID ↓
IS ↑
Lpix-recon
1
1.70
25.35
168.8
20.68
204.4
4
-
13.58
162.9
11.76
231.7
+ Lpix-con
1
0.89
17.19
183.8
14.74
218.3
4
-
10.12
189.9
10.47
247.1
+ Llat-con
1
1.32
15.40
188.3
13.14
225.1
Table 4: Ablation of loss terms on ImageNet. Loss terms are added incrementally from top to bottom.
Figure 12: Consistency optimization path from noisy latent to clean latent on the sphere, pushing the decoder to generate consistent and diverse images from right to left.
w/o cfg
w/ cfg =1.2
latent L
steps
rFID ↓
gFID ↓
IS ↑
gFID ↓
IS ↑
volume compression ratio =1.5
162×512
1
0.64
16.06
169.8
14.25
187.6
4
-
10.03
153.0
8.71
180.8
322×128
1
0.60
20.63
145.1
17.69
164.9
4
-
15.45
127.0
12.75
154.6
Table 5: Ablation on latent spatial resolution with two optimal compression ratios on ImageNet.
γ
share e
1
2
4
6
8
10
0
-
16.57
7.99
7.68
7.49
7.61
7.71
✓
16.66
7.97
5.99
7.78
10.11
12.25
1
-
16.73
8.12
9.02
12.17
15.08
18.09
✓
16.81
8.02
8.53
12.32
17.50
22.78
Table 6: Ablation on sampling schemes with few-step generation and no CFG. Results are reported with gFID ↓ on ImageNet.
Figure 13: Qualitative impact of sampling schemes on generation without CFG for CIFAR-10 (top) and ImageNet (bottom). The ✓ indicates sharing the same noise e across steps. Shared noise with γ=1 yields superior coherence and a sharp “paper art” aesthetic on ImageNet as sampling steps increase.
Figure 14: Randomly selected images generated by the Sphere encoder for ImageNet ( 256×256 ). Results are generated using Sphere-XL with 4-step sampling and CFG =1.4 .
Figure 15: Uncurated results on ImageNet ( 256×256 ). Results are generated using Sphere-XL with 4-step sampling and CFG =1.4 .
Figure 16: Uncurated results on ImageNet ( 256×256 ). Results are generated using Sphere-XL with 4-step sampling and CFG =1.4 .
Figure 17: Uncurated qualitative results on CIFAR-10 ( 32×32 ), Oxford-Flowers and Animal-Faces ( 256×256 ). Results are 2-step generation without CFG.
Figure 18: Uncurated qualitative results on CIFAR-10 ( 32×32 ), Oxford-Flowers and Animal-Faces ( 256×256 ). Results are 4-step generation without CFG.
Appendix figures & tables12 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 19: Memorization risk with longer 10 K training epochs on CIFAR-10. Each row is a different sampling run showing near-duplicate birds of the real training image (in red box).
method
steps
rFID ↓
gFID ↓
IS ↑
without CFG
sphere-l
1
0.68
16.02
9.5
2
-
4.92
10.3
4
-
1.24
10.7
6
-
1.01
10.9
8
-
1.01
10.8
Appendix
Table 7: Few-step conditional generation results on CIFAR-10 with longer 10 K training epochs.
method
cfg
steps
rFID ↓
gFID ↓
IS ↑
sphere-l
1.2
1
0.59
18.82
9.1
2
-
8.41
10.0
4
-
2.53
10.6
6
-
1.41
10.8
8
-
1.18
10.8
10
-
1.12
10.9
Appendix
Table 8: Few-step generation results on CIFAR-10 with CFG.
steps w/ cfg =1.0
steps w/ cfg =1.2
steps w/ cfg =1.4
steps w/ cfg =1.6
cfg position
1
2
4
6
8
1
2
4
6
8
1
2
4
6
8
1
2
4
6
8
enc
16.7
7.9
6.0
7.9
10.0
16.7
8.0
6.1
7.8
10.3
16.8
7.9
6.1
7.9
10.5
16.8
7.9
6.11
8.1
10.7
dec
16.7
8.0
5.9
7.8
10.1
15.0
8.3
4.7
5.1
6.2
15.4
9.3
5.0
4.5
5.0
16.4
10.2
5.7
4.7
4.8
combo
16.7
7.9
6.0
7.8
10.2
15.3
8.0
5.1
6.1
7.9
15.1
8.2
4.7
5.2
6.5
15.0
8.6
4.7
4.7
5.7
Appendix
Table 9: Ablation on CFG position . Results are reported with gFID ↓ on ImageNet. The sampling scheme is the fixed strength with sharing noise e in spheriying process across all steps.
w/o cfg
w/ cfg =1.6
base max α
mix range
steps
gFID ↓
IS ↑
gFID ↓
IS ↑
80∘
-
1
21.17
8.8
18.93
9.3
-
4
8.48
10.0
7.47
10.1
80∘
[80∘,85∘]
1
19.82
8.7
18.39
9.1
4
7.98
10.1
7.05
10.2
80∘
[80∘,89∘]
1
29.60
8.8
30.23
9.2
Appendix
Table 10: Impact of mixing a range of larger angles during training on CIFAR-10. All settings yield rFID scores in the range of 0.46–0.48 .
w/o cfg
w/ cfg =1.6
add-ons
steps
rFID ↓
gFID ↓
IS ↑
gFID ↓
IS ↑
-
1
1.20
17.56
182.5
14.88
217.8
4
-
8.73
177.6
8.05
245.0
+ BN
1
0.94
17.28
181.6
14.71
216.0
4
-
8.39
171.3
7.65
240.3
+ LSWD
1
1.01
18.95
164.4
15.47
202.1
Appendix
Table 11: Ablation on explicit uniform regularization on the spherical latent space.
w/o cfg
w/ cfg =1.6
calib by
steps
rFID ↓
gFID ↓
IS ↑
gFID ↓
IS ↑
on-the-fly
1
0.99
14.21
214.2
13.02
246.0
4
-
6.85
202.3
7.39
268.2
generated
1
0.99
14.21
214.2
13.02
246.0
images
4
-
7.30
211.1
8.08
273.9
reference
1
1.00
14.21
214.2
13.02
246.0
Appendix
Table 12: Recalibrating BN stats for inference on ImageNet.
Figure 20: Quantitative impact of volume compression ratio on ImageNet. Details in Table 13 .
compression ratio
latent L
steps
rFID ↓
gFID ↓
IS ↑
24
162×32
1
1.61
27.99
195.6
4
-
15.34
245.1
12
162×64
1
1.38
20.82
233.8
4
-
10.28
259.0
6.0
162×128
1
1.15
17.26
225.0
4
-
7.72
229.4
Appendix
Table 13: Ablation on pixel/latent volume compression ratio on ImageNet without CFG.
w/o cfg
w/ cfg =1.2
trunc α
steps
gFID ↓
IS ↑
gFID ↓
IS ↑
-
1
17.81
233.9
16.30
261.0
4
5.92
192.3
5.02
229.7
0.05
1
17.89
231.7
15.81
277.0
4
5.88
192.2
5.08
228.2
0.5
1
17.96
231.4
15.73
275.8
Appendix
Table 14: Ablation of noise prior distribution on ImageNet.
w/o cfg
w/ cfg =1.6
angle α
σ
steps
rFID ↓
gFID ↓
IS ↑
gFID ↓
IS ↑
45∘
1.0
1
0.69
69.57
31.3
59.09
39.9
4
-
80.32
18.7
73.04
21.9
80∘
5.7
1
0.87
60.14
33.4
51.73
41.3
4
-
42.72
39.3
34.14
54.3
81∘
6.3
1
0.94
47.68
40.4
40.11
51.1
Appendix
Table 15: Detailed quantitative results for the impact of the angle α on ImageNet for Figure 11 .
hyperparameter ╲ dataset
cifar-10
animal-faces
oxford-flowers
imagenet
image size
32
256
256
256
batch size
256
256
256
256
learning rate (lr)
1×10−4
1×10−4
1×10−4
1×10−4
lr decay schedule
cosine
cosine
cosine
cosine
min lr
1×10−6
1×10−6
1×10−6
1×10−6
weight decay
0.0
0.0
0.0
0.0
Appendix
Table 16: Training hyperparameters and model details for main experiments.
Sphere Encoder is an autoencoder that generates images by decoding random points from a high-dimensional latent sphere. We identify two limitations of the original formulation that reduce its generation quality. First, random points concentrate near the equator relative to the pole on an encoded latent, but the training rotation never reaches this region, leaving a gap that limits one-step generation. Second, training for generation with pixel-wise reconstruction loss encourages the decoder to average over plausible images, producing blurry images that lack high-frequency details. We present Sphere Encoder 2 to address both limitations, substantially improving image generation quality while maintaining the speed and simplicity of a autoencoder. Models are released at https://github.com/kaiyuyue/sphere2.
Kaiyu Yue, Sean McLeish, Ruchit Rawal +3
University of Maryland · Lawrence Livermore National Laboratory · Cornell University
Few-step image generation has seen rapid progress, with consistency and meanflow-based methods significantly reducing the number of sampling steps. Despite their low inference cost, these approaches often suffer from training instability and limited scalability. Sphere Encoder is a recent alternative that produces high-quality images in only a few steps; however, it requires repeated transitions between the pixel space and latent space during inference while jointly optimizing reconstruction and generation within a single architecture. This design leads to computational inefficiency and objective conflict between reconstruction and generation. To address these limitations, we decouple the framework into a fixed pretrained image encoder and a separate latent denoising model trained entirely in a spherical latent space. Our approach eliminates repeated pixel-space operations during training and inference, improving efficiency and allowing reconstruction and generation to specialize independently. On Animal-Faces, Oxford-Flowers and ImageNet-1K datasets, our method significantly outperforms Sphere Encoder in both generation quality and inference speed, while achieving competitive results against strong few-step and multi-step baselines.
Tung Do, Thuan Hoang Nguyen, Hao Li
Mohamed Bin Zayed University of Artificial Intelligence, UAE
Diffusion models generate samples through a multi-step denoising trajectory, yet condition every step on the same instruction, so the trajectory cannot be addressed at the level of individual operations. We introduce Dancing Diffusion, which assigns each span of timesteps a dedicated continuous condition block and thereby turns conditioning into a latent program. A compiler maps text features into this program, and a fixed pretrained generator executes its blocks over successive sampling intervals. The trajectory can then dance, keeping its executed history while its continuation is redirected. A shared prefix is executed once and reused, and a later operation is rewritten while content fixed by earlier operations is preserved. The compiler is trained through the images it produces, with visual feedback on both the requested change and the retained content. On SANA, reusing an executed prefix preserves markedly more of the scene than regenerating from noise at a similar strength of edit, learned conditions preserve more background than native prompt switching from the same saved state, and the learned program improves generation quality over native SANA. Later branches weaken the edit, which leaves semantic control over individual operations limited. By converting a single-instruction trajectory into a program of addressable operations, Dancing Diffusion lays a foundation for structured intermediate computation in diffusion models.
Cui Enhe, Jinyue Yang, Bojian Yin +1
Renmin University of China · Institute of Automation, Chinese Academy of Sciences