We propose a landmark-constrained algorithm, LA-VDM (Landmark Accelerated Vector Diffusion Maps), to accelerate the Vector Diffusion Maps (VDM) framework built upon the Graph Connection Laplacian (GCL), which captures pairwise connection relationships within complex datasets. LA-VDM introduces a novel two-stage normalization that effectively address nonuniform sampling densities in both the data and the landmark sets. Under a manifold model with the frame bundle structure, we show that we can accurately recover the parallel transport with landmark-constrained diffusion from a point cloud, and hence asymptotically LA-VDM converges to the connection Laplacian. The performance and accuracy of LA-VDM are demonstrated through experiments on simulated datasets and an application to nonlocal image denoising.
Figures & tables
Figure 1. Illustration of a potential issue in estimating parallel transport from x to y via landmark diffusion: different paths yield different parallel-transported vectors at y .
Figure 2. Illustration of parallel transport from s1 to s2 on the distorted sphere. The vector attached at s1 is transported along the surface to s2 using different size of landmark.
Figure 3. From left to right: a comparison of computational time between VDM and (1/2,0) -LA-VDM with different landmark sizes, he difference ratio of the 1st, 3rd, 5th eigenvalues between VDM and (1/2,0) -LA-VDM, the cosine similarity of the 1st, 3rd, 5th eigenvectors between VDM and (1/2,0) -LA-VDM.
Figure 4. Plot of the first, third, and fifth eigenvector fields eigenvectors, for the Klein bottle on the parameter space P . From top to bottom: first, third, and fifth eigen vector fields, and from left to right column: landmark set size 256, 1024, and 4096.
Figure 5. Plot of Il,2 , where l=1,3,5 , for the Klein bottle on the parameter space P ; that is, plot (ϕ−1(si),Il,2(i)) . From top to bottom: first, third, and fifth eigen vector fields, and from left to right column: landmark set size 256, 1024, and 4096.
Figure 6. Plot of Il,a , where l=1,3,5 , for the Klein bottle on the parameter space P ; that is, plot (ϕ−1(si),Il,a(i)) . From top to bottom: first, third, and fifth eigen vector fields, and from left to right column: landmark set size 256, 1024, and 4096.
Figure 7. Plot of Il,m , where l=1,3,5 , for the Klein bottle on the parameter space P ; that is, plot (ϕ−1(si),Il,m(i)) . From top to bottom: first, third, and fifth eigen vector fields, and from left to right column: landmark set size 256, 1024, and 4096.
Eigen
Metric
Landmark size
128
512
2048
1st
I1,2
0.108 ± 0.045
0.036 ± 0.014*
0.026 ± 0.010*
I1,a
0.639 ± 0.378
0.549 ± 0.339*
0.342 ± 0.204*
I1,m
1.262 ± 0.686
1.029 ± 0.676*
0.303 ± 0.179*
3rd
I3,2
0.999 ± 0.001
0.999 ± 0.001*
0.999 ± 0.001*
Table 1. Performance comparison across different eigenvector with different landmark sizes.
Figure 8. From left to right: the difference ratio of the 2nd, 4th, 6th non-trivial eigenvalues between VDM and (β,0) -LA-VDM, the inner product between the 2nd, 4th, 6th non-trivial eigenvectors of VDM and (β,0) -LA-VDM, the difference of the 2nd, 4th, 6th non-trivial eigenvectors of VDM and (β,0) -LA-VDM.
Figure 9. From left to right: the difference ratio of the 2nd, 4th, 6th non-trivial eigenvalues between VDM with α=1 and (1/2,α) -LA-VDM, the inner product between the 2nd, 4th, 6th non-trivial eigenvectors of VDM with α=1 and (1/2,α) -LA-VDM, the difference of the 2nd, 4th, 6th non-trivial eigenvectors of VDM with α=1 and (1/2,α) -LA-VDM.
Figure 10. From left to right: the difference ratio of eigenvalues between VDM and LA-VDM, the inner product between eigenvectors of VDM and LA-VDM, the L2 difference of eigenvectors of VDM and LA-VDM.
Masked Discrete Diffusion Models (MDMs) have achieved strong performance across a wide range of multimodal tasks, including image understanding, generation, and editing. However, their inference speed remains suboptimal due to the need to repeatedly process redundant masked tokens at every sampling step. In this work, we propose Sparse-LaViDa, a novel modeling framework that dynamically truncates unnecessary masked tokens at each inference step to accelerate MDM sampling. To preserve generation quality, we introduce specialized register tokens that serve as compact representations for the truncated tokens. Furthermore, to ensure consistency between training and inference, we design a specialized attention mask that faithfully matches the truncated sampling procedure during training. Built upon the state-of-the-art unified MDM LaViDa-O, Sparse-LaViDa achieves up to a 2x speedup across diverse tasks including text-to-image generation, image editing, and mathematical reasoning, while maintaining generation quality.
Diffusion models have achieved remarkable success in generating high-fidelity content but suffer from slow, iterative sampling, resulting in high latency that limits their use in interactive applications. We introduce DRiffusion, a parallel sampling framework that parallelizes diffusion inference through a draft-and-refine process. DRiffusion employs skip transitions to generate multiple draft states for future timesteps and computes their corresponding noises in parallel, which are then used in the standard denoising process to produce refined results. Theoretically, our method achieves an acceleration rate of n1 or n+12, depending on whether the conservative or aggressive mode is used, where n denotes the number of devices. Empirically, DRiffusion attains 1.4×-3.7× speedup across multiple diffusion models while incur minimal degradation in generation quality: on MS-COCO dataset, both FID and CLIP remain largely on par with those of the original model, while PickScore and HPSv2.1 show only minor average drops of 0.17 and 0.43, respectively. These results verify that DRiffusion delivers substantial acceleration and preserves perceptual quality.
Runsheng Bai, Chengyu Zhang, Yangdong Deng
CSAIL, MIT · IST, Nanjing University · School of Software, Tsinghua University; FuturististAI Lab, Shanghai Tsinghua International Innovation Center
High definition map generation is essential for autonomous driving, yet remains a labor-intensive process at scale. We present MapDreamer, a generative diffusion model that synthesizes lane-level vector maps with explicit topology directly from a single aerial image. MapDreamer learns a compact latent representation of lane centerlines and their topological relations using a variational autoencoder and predicts graphs with a transformer-based latent diffusion model. To align generated maps with the observed scene, we condition each denoising step on dense aerial features injected through cross-attention. To handle the varying number of lanes across scenes, we propose a lane cardinality module paired with background ghost lane latents, a learned buffer that prevents slot collapse during diffusion. Furthermore, we introduce a sliding-window global graph aggregation strategy that stitches local tiles into city-scale maps while preserving connectivity through encoded lane boundaries. Experiments on UrbanLaneGraph derived from Argoverse 2 show improved geometric and topological fidelity over non-generative baselines.
Julian Brandes, Philipp Crocoll, Wolfram Burgard
Department CSAI at University of Technology Nuremberg, Nuremberg, Germany · Robert Bosch GmbH, Stuttgart