Pooling Representation Autoencoders for Efficient Diffusion

Ramón Calvo-González; Youssef Saied; François Fleuret

cs.CVOct 7, 2026

Pooling Representation Autoencoders for Efficient Diffusion

Authors: Ramón Calvo-González, Youssef Saied, François Fleuret

Organizations: University of Geneva · University of Geneva and Meta

Abstract

Representation Autoencoders (RAEs) generate images from pre-trained visual fea- tures, but their dense token grids make generative modeling expensive. Motivated by local feature correlations, we introduce PoolDINO, a learned affine pooling operator that merges neighboring tokens. Training the pooling operator jointly with the RGB decoder preserves the standard two-stage RAE procedure without a separate feature auto-encoder. On ImageNet-256, 4x token compression retains comparable generation quality under internal guidance, while 16x compression trades some quality for greater efficiency. At a fixed budget of 100 sampling steps, latent-sampling throughput increases by 3.7x and 9.0x, respectively, relative to the unpooled baseline. Classification and dense prediction evaluations show that comparable guided generation quality can coexist with weaker performance on other tasks.

Figures & tables

Panel of Figure 1 — Figure 1: Generation quality versus latent-sampling throughput on an NVIDIA H100 NVL at batch size 128. PoolDINO and the RAEv2 reference use Internal Guidance (IG) with 100 Euler steps. Red points use 80 training epochs; gold points use extended training (180 epochs for $2\times 2$ and 300 for $4\times 4$ ). Diamonds pair published FIDs with measured sampling rates. Appendix B details the measurement protocols and shows that reducing to 50 sampling steps doubles throughput while maintaining comparable generation quality.

Spatial pooling	Tokens	rFID $\downarrow$	sFID $\downarrow$	PSNR $\uparrow$	LPIPS $\downarrow$
RAEv2 baseline	256	0.32	2.29	22.74	0.15
Learned $2{\times}2$	64	0.36	2.61	22.25	0.17
Learned $2{\times}4$	32	0.39	2.76	21.88	0.18
Learned $4{\times}2$	32	0.39	2.82	21.85	0.18
Learned $4{\times}4$	16	0.41	2.99	21.45	0.19
Average $2{\times}2$	64	0.65	4.97	19.58	0.25

Table 1: Reconstruction on the ImageNet-1K

256\times 256

validation set, grouped by pooling method. All RGB decoders process 256 tokens after repetition.

Panel of Figure 3 — Figure 3: Curated samples across spatial compression levels, with all generators trained for 80 epochs. Samples are selected independently across columns. Sampling uses 100 Euler steps and each model’s selected IG-only scale. Appendix G provides randomly selected samples without quality filtering.

		Unguided		IG		IG + CFG
Spatial pooling	Tokens	FID $\downarrow$	IS $\uparrow$	FID $\downarrow$	IS $\uparrow$	FID $\downarrow$	IS $\uparrow$
RAEv2 baseline	256	1.53	226.63	1.08	262.00	1.07	267.15
Learned $2{\times}2$	64	3.00	184.49	1.09	250.36	1.07	268.50
Learned $2{\times}4$	32	4.91	161.42	1.19	249.58	1.16	273.06
Learned $4{\times}2$	32	4.97	159.67	1.21	249.96	1.19	273.98
Learned $4{\times}4$	16	8.16	132.67	1.44	247.07	1.35	282.29

Table 2: ImageNet-256 generation at 100 Euler steps. Models train for 80 epochs. We report generation FID and Inception Score (IS; Salimans et al. 2016 ). Guided columns report the lowest-FID settings from our guidance scale sweeps; the corresponding scales are in Table 18 . Best and second-best metrics in each column are bold and underlined.

		Unguided		IG
Pooling	Epochs	FID $\downarrow$	IS $\uparrow$	FID $\downarrow$	IS $\uparrow$
$1\times 1$ (unpooled)	80	1.53	226.63	1.08	262.00
$2\times 2$	80	3.00	184.49	1.09	250.36
$2\times 2$	180	2.78	192.37	1.05	272.00
$4\times 4$	80	8.16	132.67	1.44	247.07
$4\times 4$	300	7.19	146.13	1.29	258.04

Table 3: Effect of extended training, evaluated with 100 Euler steps at the guidance settings in Table 18 . The unpooled 80-epoch model is included as a reference; bold marks the stronger result within each pooling window. Appendix A.2 gives longer runs and finer IG sweeps.

Panel of Figure 4 — Figure 4: Curated comparisons of 80-epoch and extended training. Class conditions and initial noise are matched within each pair. All samples use 100 Euler steps and IG alone: scales 1.75/2.00 for the 80/180-epoch $2\times 2$ models, and 2.75 for both $4\times 4$ models.

		ImageNet-1K	ADE20K	NYUv2
Spatial pooling	Window	Linear top-1 (%) $\uparrow$	mIoU (%) $\uparrow$	AbsRel $\downarrow$
Unpooled	$1\times 1$	85.31	46.86	0.0817
Learned	$2\times 2$	83.47	39.38	0.0895
Average	$2\times 2$	85.33	42.59	0.0869
Learned	$4\times 4$	80.80	38.61	0.1022
Average	$4\times 4$	85.33	36.76	0.0997

Table 4: Classification and dense prediction from frozen representations. Dense task models train from scratch. Bold marks the stronger pooling rule at each compression rate.

Appendix figures & tables35 assets

Supplementary material from the paper’s appendix.

Appendix

Pooling window	Latent grid	Tokens	Compression	$\kappa$
$1\times 1$ (control)	$16\times 16$	256	$1\times$	8
$2\times 2$	$8\times 8$	64	$4\times$	4
$2\times 4$	$8\times 4$	32	$8\times$	$\sqrt{8}$
$4\times 2$	$4\times 8$	32	$8\times$	$\sqrt{8}$
$4\times 4$	$4\times 4$	16	$16\times$	2

Appendix

Table 5: Latent grids. Compression is relative to the 256-token control.

Hyperparameter	Image decoder	Flow encoder	Flow decoder
Transformer blocks	28	28	2
Hidden size	1,152	1,440	2,048
MLP width	4,096	3,840	5,461
Attention heads	16	20	16
Time tokens	–	4	–
Class tokens	–	8	–

Appendix

Table 6: Model architecture hyperparameters.

Hyperparameter	Decoder Stage	Flow-Model Stage
Training epochs	16	80
Training steps	40,032	100,080
Global batch size	512	1,024
Optimizer	AdamW	Muon (AdamW fallback)
Base learning rate	$2\times 10^{-4}$	$2\times 10^{-4}$
Learning rate schedule	Cosine decay to $2\times 10^{-5}$	Constant through epoch 25; linear decay to $2\times 10^{-5}$ at epoch 50

Appendix

Table 7: Optimization hyperparameters for both training stages.

Window	Tokens	Generator	Internal head	Repr. path	Decoder	Unguided generation
$1\times 1$	256	473.182G	2.887G	0.756G	224.216G	47.542T
$2\times 2$	64	128.653G	0.722G	1.292G	224.216G	13.090T
$2\times 4$	32	72.531G	0.361G	1.292G	224.216G	7.477T
$4\times 4$	16	44.612G	0.180G	1.292G	224.216G	4.685T

Appendix

Table 8: Estimated forward FLOPs per image, counting a multiply-add as two operations. Component columns report one evaluation. “Internal head” is the additional cost of returning the early clean-latent prediction. “Representation path” includes the dense-representation projection and pooling operation. Unguided generation counts 100 base generator evaluations and one image-decoder evaluation, excluding auxiliary heads and additional CFG evaluations.

	180 epochs		222 epochs
IG scale	FID $\downarrow$	IS $\uparrow$	FID $\downarrow$	IS $\uparrow$
1.000	2.7805	192.37	2.7682	193.79
1.250	1.7069	218.79	1.7269	220.06
1.500	1.2237	240.43	1.2330	242.09
1.750	1.0603	257.87	1.0645	259.57
1.875	1.0462	265.43	1.0476	266.27

Appendix

Table 9: IG sweeps for

2\times 2

learned pooling at 180 and 222 epochs. Bold marks the lowest observed FID at each duration.

	300 epochs		390 epochs
IG scale	FID $\downarrow$	IS $\uparrow$	FID $\downarrow$	IS $\uparrow$
1.000	7.1942	146.13	6.7782	150.30
1.250	4.7407	171.29	4.4667	176.07
1.500	3.1969	194.26	3.0450	198.28
1.750	2.2363	214.17	2.1802	218.03
2.000	1.7026	229.57	1.6962	233.37

Appendix

Table 10: IG sweeps for

4\times 4

learned pooling at 300 and 390 epochs. Bold marks the lowest observed FID at each duration.

Panel of Figure 6 — Figure 6: Quality–throughput comparison with both guidance settings on an H100 NVL at batch size 128. Our 80-epoch models use IG alone (solid, filled) or CFG+IG (dashed, hollow), with FID evaluated at 100 Euler steps. Point labels give token compression; black circles denote the unpooled RAEv2 reference. Literature baselines and timing conventions match Figure 1 ; full-sampling throughput excludes image decoding.

Panel of Figure 7 — Figure 7: Inception Score versus latent-sampling throughput on an H100 NVL at batch size 128. PoolDINO and the unpooled RAEv2 reference use IG alone at 100 Euler steps, including the extended-training checkpoints. IS is taken at the FID-selected guidance settings, not maximized separately.

			FID $\downarrow$		Latent samples/s $\uparrow$
Pooling	Epochs	$s_{\mathrm{IG}}$	100 steps	50 steps	100 steps	50 steps
$2\times 2$	80	1.75	1.0890	1.1164	$24.16\pm 0.05$	$48.44\pm 0.17$
$2\times 2$	180	2.00	1.0525	1.0629	$24.16\pm 0.05$	$48.44\pm 0.17$
$2\times 4$	80	2.00	1.1913	1.2283	$40.10\pm 0.07$	$80.42\pm 0.33$
$4\times 4$	80	2.75	1.4442	1.4429	$58.46\pm 0.20$	$117.13\pm 0.38$
$4\times 4$	300	2.75	1.2882	1.2981	$58.46\pm 0.20$	$117.13\pm 0.38$

Appendix

Table 11: IG-only generation with 100 versus 50 Euler steps. Throughput is latent samples/s on an H100 NVL at batch size 128;

\pm

reports timing standard deviation.

Panel of Figure 8 — Figure 8: Generation quality versus latent-sampling throughput with 50-step sampling for PoolDINO, using IG alone on an H100 NVL at batch size 128. Red points show the 80-epoch models; gold points show extended training. The RAEv2 reference uses IG with 100 steps. Literature points, including FlatDINO, retain their published FIDs and measured throughput under their respective sampling protocols.

Panel of Figure 9 — Figure 9: Sampling-step ablation for the $4\times 4$ generator trained for 300 epochs. Gold shows FID (left axis); red shows IS (right axis). The IG scale is fixed at 2.75 rather than retuned for each step count.

Panel of Figure 10 — Figure 10: Denoiser forward-pass speed on a single GPU, using the flow-model architecture in Table 6 . Legend entries give pooling windows and token compression. Each point is the mean of 30 measurements averaging 20 forward calls; error bars show one standard deviation and are mostly smaller than the markers. Benchmarks use BF16 computation and include host dispatch and synchronization, but not end-to-end image generation.

Panel of Figure 11 — Figure 11: Generator forward–backward throughput on a single GPU. Points show mean iterations/s across 30 measurements of 20 iterations. Timing includes the forward pass, main-prediction MSE loss, backward pass, and dispatch/synchronization; it excludes optimizer updates, auxiliary losses, and the encoder/decoder. The uncompressed model runs out of memory at batch size 256 on both GPUs.

Window	Learned	Average	PCA	Random	Learned	Average	PCA	Random
	k-NN				Linear probe
Uncompressed $z$	76.03				85.31
$2\times 2$	72.16	76.00	76.67	$75.78\pm 0.06$	83.47	85.33	84.35	$\underline{84.63\pm 0.06}$
$2\times 4$	68.50	76.00	76.58	$75.77\pm 0.03$	82.35	85.33	84.10	$\underline{84.50\pm 0.04}$
$4\times 2$	68.17	76.00	76.59	$75.68\pm 0.05$	82.35	85.34	84.12	$\underline{84.43\pm 0.07}$
$4\times 4$	63.22	76.00	76.39	$75.68\pm 0.04$	80.80	85.33	83.77	$\underline{84.21\pm 0.04}$

Appendix

Table 12: ImageNet-1K k-NN and linear-probe top-1 accuracy (%). The uncompressed RAEv2 representation

z

is included as a reference. Best and second-best methods at each compression rate are bold and underlined.

Spatial pooling	Best epoch	Val. loss $\downarrow$	mIoU $\uparrow$	Mean acc. $\uparrow$	Pixel acc. $\uparrow$
Uncompressed	75	0.671	46.860	58.060	81.260
Learned $2\times 2$	75	0.807	39.380	50.100	77.480
Average $2\times 2$	65	0.735	42.591	53.477	78.905
Learned $4\times 4$	80	0.863	38.610	48.850	77.780
Average $4\times 4$	75	0.866	36.758	46.969	75.715

Appendix

Table 13: ADE20K semantic segmentation with task models trained from scratch. Accuracy metrics are percentages.

Spatial pooling	Best epoch	AbsRel $\downarrow$	RMSE $\downarrow$	Log RMSE $\downarrow$	SiLog $\downarrow$	$\delta_{1}$ $\uparrow$	$\delta_{2}$ $\uparrow$	$\delta_{3}$ $\uparrow$
Uncompressed	12	0.082	0.409	0.122	0.122	94.170	99.030	99.780
Learned $2\times 2$	21	0.090	0.455	0.134	0.134	92.780	98.700	99.720
Average $2\times 2$	14	0.087	0.434	0.131	0.131	93.200	98.720	99.730
Learned $4\times 4$	27	0.102	0.490	0.148	0.148	90.440	98.260	99.610
Average $4\times 4$	15	0.100	0.486	0.149	0.149	90.580	98.060	99.560

Appendix

Table 14: NYUv2 monocular depth estimation with task models trained from scratch. The

\delta

metrics are percentages.

Spatial pooling	Tokens	Compression	Best epoch	Val. loss $\downarrow$	mIoU $\uparrow$	Mean acc. $\uparrow$	Pixel acc. $\uparrow$
Uncompressed	256	$1\times$	80	0.694	47.810	58.850	81.770
Learned $2\times 2$	64	$4\times$	60	0.709	45.380	56.420	81.010
Learned $4\times 4$	16	$16\times$	80	0.788	42.500	53.240	79.960

Appendix

Table 15: ADE20K semantic segmentation with task models initialized from the corresponding RGB decoder. Accuracy metrics are percentages.

Spatial pooling	Best epoch	AbsRel $\downarrow$	RMSE $\downarrow$	Log RMSE $\downarrow$	SiLog $\downarrow$	$\delta_{1}$ $\uparrow$	$\delta_{2}$ $\uparrow$	$\delta_{3}$ $\uparrow$
Uncompressed	14	0.081	0.411	0.123	0.123	94.330	98.980	99.750
Learned $2\times 2$	27	0.089	0.456	0.133	0.133	92.800	98.720	99.700
Learned $4\times 4$	24	0.101	0.495	0.147	0.147	90.610	98.220	99.610

Appendix

Table 16: NYUv2 monocular depth estimation with task models initialized from the corresponding RGB decoder. The

\delta

metrics are percentages.

	Unguided		CFG		IG		CFG + IG
Variant	FID $\downarrow$	IS $\uparrow$	FID $\downarrow$	IS $\uparrow$	FID $\downarrow$	IS $\uparrow$	FID $\downarrow$	IS $\uparrow$
$1\times 1$	1.53	226.63	1.45	237.80	1.08	262.00	1.07	267.15
$2\times 2$	3.00	184.49	1.99	228.10	1.09	250.36	1.07	268.50
$2\times 4$	4.91	161.42	2.33	238.80	1.19	249.58	1.16	273.06
$4\times 2$	4.97	159.67	2.41	237.63	1.21	249.96	1.19	273.98
$4\times 4$	8.16	132.67	2.87	249.72	1.44	247.07	1.35	282.29

Appendix

Table 17: ImageNet-256 generation at 100 Euler steps. Models train for 80 epochs, except the extended-training

2\times 2

(180 epochs) and

4\times 4

(300 epochs) variants. Guided columns use the settings in Table 18 ; Appendix A.2 separately reports longer runs and finer IG sweeps. – denotes an unevaluated setting. Best and second-best metrics in each column are bold and underlined.

	CFG	IG	CFG + IG
Variant	$s_{\mathrm{CFG}}$	$s_{\mathrm{IG}}$	$s_{\mathrm{CFG}}$	$s_{\mathrm{IG}}$
$1\times 1$	3.00	1.75	2.50	1.78
$2\times 2$	3.00	1.75	1.75	1.75
$2\times 4$	3.00	2.00	1.50	2.00
$4\times 2$	3.00	2.00	1.50	2.00
$4\times 4$	3.00	2.75	1.75	2.25

Appendix

Table 18: Guidance scales selected for Tables 2 , 3 , and 17 . For CFG alone,

s_{\mathrm{IG}}=1

; for IG alone,

s_{\mathrm{CFG}}=1

. Both scales are one for unguided sampling.

Method	Euler steps	Guidance scale	Guidance interval	Neutral value
Unguided	100	–	–	CFG 1
Internal guidance	100	Swept	$[0,0.9]$	1
Encoder-reconstruction guidance	100	Swept	$[0,1]$	0

Appendix

Table 19: Sampling settings for the guidance ablations. Intervals use noise-to-data time:

t=0

is noise and

t=1

is clean data.

Panel of Figure 12 — Figure 12: Isolated guidance-scale sweeps on ImageNet-256. Top: FID on a logarithmic scale. Bottom: Inception Score. Missing points in the corrected $2\times 2$ sweeps are left blank.

	Encoder-reconstruction guidance		Internal guidance
Variant	FID $\downarrow$	IS $\uparrow$	FID $\downarrow$	IS $\uparrow$
$2\times 2$	1.06	272.83	1.07	268.50
$2\times 4$	1.17	279.68	1.16	273.06
$4\times 2$	1.20	280.14	1.19	273.98
$4\times 4$	1.35	295.39	1.35	282.29

Appendix

Table 20: Metrics at the lowest-FID point in each joint guidance sweep for the 80-epoch models. Both auxiliary methods are combined with CFG.

Panel of Figure 13 — Figure 13: Joint CFG and encoder-reconstruction guidance search. Squares show evaluated 100-step configurations; the black outline marks the lowest FID in each panel.

Panel of Figure 14 — Figure 14: Inception Score for the joint CFG and encoder-reconstruction guidance search. The black outline marks the highest score in each panel.

Panel of Figure 15 — Figure 15: Joint CFG and internal-guidance search. Squares show evaluated 100-step configurations; the black outline marks the lowest FID in each panel.

Panel of Figure 16 — Figure 16: Inception Score for the joint CFG and internal-guidance search. The black outline marks the highest score in each panel.

Window	Average alignment	PCA alignment	Energy captured (% of PCA)
$2\times 2$	0.5000	0.2798	67.60
$2\times 4$	0.3530	0.2114	52.16
$4\times 2$	0.3501	0.2082	52.05
$4\times 4$	0.2268	0.1524	38.16

Appendix

Table 21: Learned pooling row-space analysis. Alignment scores are adjusted so that zero indicates the overlap expected between random subspaces of the same dimension and one indicates identical subspaces. Energy captured is the squared validation feature energy preserved by the learned pooling operator’s row space (after centering with the training mean), expressed as a percentage of that captured by PCA with the same output dimension.

Window	Random	Raw	Adjusted	Raw	Adjusted	Energy (% PCA)
		Average overlap		PCA overlap
$2\times 2$	0.2500	0.6250	0.5000	0.4598	0.2798	67.60
$2\times 4$	0.1250	0.4339	0.3530	0.3100	0.2114	52.16
$4\times 2$	0.1250	0.4313	0.3501	0.3072	0.2082	52.05
$4\times 4$	0.0625	0.2751	0.2268	0.2054	0.1524	38.16

Appendix

Table 22: Complete learned pooling row-space results. “Random” is the expected raw overlap of random subspaces of the same dimension. Energy captured is reported as a percentage of rate-matched PCA.

Figure 17: Unpooled RAEv2 reference ( $1\times 1$ ), trained for 80 epochs, with $s_{\mathrm{IG}}=1.75$ and no CFG. Samples are randomly selected without quality filtering.

Figure 18: PoolDINO with $2\times 2$ learned pooling ( $4\times$ token compression), trained for 80 epochs, with $s_{\mathrm{IG}}=1.75$ and no CFG. Samples are randomly selected without quality filtering.

Figure 19: PoolDINO with $2\times 4$ learned pooling ( $8\times$ token compression), trained for 80 epochs, with $s_{\mathrm{IG}}=2.00$ and no CFG. Samples are randomly selected without quality filtering.

Figure 20: PoolDINO with $4\times 4$ learned pooling ( $16\times$ token compression), trained for 80 epochs, with $s_{\mathrm{IG}}=2.75$ and no CFG. Samples are randomly selected without quality filtering.

Figure 21: PoolDINO with $2\times 2$ learned pooling and extended training ( $4\times$ token compression), trained for 180 epochs, with $s_{\mathrm{IG}}=2.00$ and no CFG. Samples are randomly selected without quality filtering.

Figure 22: PoolDINO with $4\times 4$ learned pooling and extended training ( $16\times$ token compression), trained for 300 epochs, with $s_{\mathrm{IG}}=2.75$ and no CFG. Samples are randomly selected without quality filtering.

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