![](bg9.png)
Figure 5: Uncurated generated samples images from our
flow model.
6 CONCLUSION
With a parallel inversion approach, we present a k × k
invertible convolution for Normalizing flow models.
We utilize it to develop a model with highly efficient
sampling pass, normalizing flow architecture. We
implement our parallel algorithm on GPU and pre-
sented benchmarking results, which show a signif-
icant enhancement in forward and sampling speeds
when compared to alternative methods for k × k in-
vertible convolution.
REFERENCES
Behrmann, J., Grathwohl, W., Chen, R. T., Duvenaud,
D., and Jacobsen, J.-H. (2019). Invertible residual
networks. In International Conference on Machine
Learning, pages 573–582. PMLR.
Brock, A., Donahue, J., and Simonyan, K. (2019). Large
scale GAN training for high fidelity natural image
synthesis. In International Conference on Learning
Representations.
Deng, L. (2012). The mnist database of handwritten digit
images for machine learning research. IEEE Signal
Processing Magazine, 29(6):141–142.
Dinh, L., Krueger, D., and Bengio, Y. (2014). Nice: Non-
linear independent components estimation. arXiv
preprint arXiv:1410.8516.
Dinh, L., Sohl-Dickstein, J., and Bengio, S. (2017). Density
estimation using real nvp. In International Conference
on Learned Representations.
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B.,
Warde-Farley, D., Ozair, S., Courville, A., and Ben-
gio, Y. (2014a). Generative adversarial nets. In
Ghahramani, Z., Welling, M., Cortes, C., Lawrence,
N., and Weinberger, K., editors, Advances in Neural
Information Processing Systems, volume 27. Curran
Associates, Inc.
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B.,
Warde-Farley, D., Ozair, S., Courville, A., and Ben-
gio, Y. (2014b). Generative adversarial nets. Advances
in neural information processing systems, 27.
Hazami, L., Mama, R., and Thurairatnam, R. (2022).
Efficient-vdvae: Less is more. arXiv preprint
arXiv:2203.13751.
Ho, J., Chen, X., Srinivas, A., Duan, Y., and Abbeel, P.
(2019). Flow++: Improving flow-based generative
models with variational dequantization and architec-
ture design. In International Conference on Machine
Learning, pages 2722–2730. PMLR.
Ho, J., Jain, A., and Abbeel, P. (2020). Denoising diffusion
probabilistic models. Advances in Neural Information
Processing Systems, 33:6840–6851.
Hoogeboom, E., Van Den Berg, R., and Welling, M.
(2019). Emerging convolutions for generative normal-
izing flows. In International Conference on Machine
Learning, pages 2771–2780. PMLR.
Keller, T. A., Peters, J. W., Jaini, P., Hoogeboom, E., Forr
´
e,
P., and Welling, M. (2021). Self normalizing flows.
In International Conference on Machine Learning,
pages 5378–5387. PMLR.
Kingma, D. P. and Ba, J. (2015). Adam: A method for
stochastic optimization. In Bengio, Y. and LeCun,
Y., editors, 3rd International Conference on Learn-
ing Representations, ICLR 2015, San Diego, CA, USA,
May 7-9, 2015, Conference Track Proceedings.
Kingma, D. P. and Dhariwal, P. (2018). Glow: Generative
flow with invertible 1x1 convolutions. Advances in
neural information processing systems, 31.
Kingma, D. P. and Welling, M. (2013). Auto-encoding vari-
ational bayes. arXiv preprint arXiv:1312.6114.
Kingma, D. P., Welling, M., et al. (2019). An introduction
to variational autoencoders. Foundations and Trends®
in Machine Learning, 12(4):307–392.
Kobyzev, I., Prince, S. J., and Brubaker, M. A. (2020). Nor-
malizing flows: An introduction and review of current
methods. IEEE transactions on pattern analysis and
machine intelligence, 43(11):3964–3979.
Krizhevsky, A. (2009). Learning multiple layers of features
from tiny images.
Liu, Z., Luo, P., Wang, X., and Tang, X. (2015). Deep
learning face attributes in the wild. In Proceedings
of the IEEE international conference on computer vi-
sion, pages 3730–3738.
Lu, Y. and Huang, B. (2020). Woodbury transformations
for deep generative flows. Advances in Neural Infor-
mation Processing Systems, 33:5801–5811.
Ma, X., Kong, X., Zhang, S., and Hovy, E. (2019). Macow:
Masked convolutional generative flow. Advances in
Neural Information Processing Systems, 32.
Meng, C., Zhou, L., Choi, K., Dao, T., and Ermon, S.
(2022). Butterflyflow: Building invertible layers with
butterfly matrices. In International Conference on
Machine Learning, pages 15360–15375. PMLR.
Nagar, S., Dufraisse, M., and Varma, G. (2021). CInc flow:
Characterizable invertible 3$\times$3 convolution. In
The 4th Workshop on Tractable Probabilistic Model-
ing.
Nash, C., Ganin, Y., Eslami, S. A., and Battaglia, P. (2020).
Polygen: An autoregressive generative model of 3d
meshes. In International conference on machine
learning, pages 7220–7229. PMLR.
Oord, A. v. d., Dieleman, S., Zen, H., Simonyan, K.,
Vinyals, O., Graves, A., Kalchbrenner, N., Senior,
A., and Kavukcuoglu, K. (2016). Wavenet: A
VISAPP 2023 - 18th International Conference on Computer Vision Theory and Applications
346