Manifold-aware training
Discrete tokens are projected into a continuous parameterized manifold. Forward diffusion produces noisy latents; a DiT predicts logits that are supervised through CE and manifold-space MSE losses.
Research project · 2026
MINDDiffusion on thedata manifold.
Image generation with explicit modeling of data manifold geometry.
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Method · At a glance
Diffuse through a
parameterized manifold.
MIND explicitly brings the geometry of the image data manifold into a continuous diffusion model.
A tokenizer first maps images to discrete patch tokens. Their embeddings define a compact parameterization space in which the score network learns to denoise, reducing the metric entropy of the learning problem while retaining parallel generation.
Multi-stage inference
Sampling changes with timestep: differentiable soft sampling, entropy-driven hybrid sampling, and greedy projection guide the latent toward valid discrete tokens before decoding.
One-step FD distillation
Conditional and unconditional predictions are combined by CFG. A greedy straight-through estimator preserves gradients through token selection and the decoder to optimize the FD loss.
One-step inference
The distilled model maps initial noise to token logits in one network evaluation. Greedy sampling and the tokenizer decoder directly produce the final image.
Lower metric entropyExplicit manifold parameterization
Soft top-kEnd-to-end differentiable token projection
High-frequency branchesReduced transformer spectral bias
Greedy STE + FDDifferentiable one-step generation
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Architecture · Key ideas
Discrete structure.
Continuous motion.
MIND inserts manifold-aware structure where a continuous diffusion transformer needs it most—inside the score function itself.
Discrete patch tokenization
Structural anchors form a compact parameterization of the image manifold.
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Soft top-k aggregation
A differentiable bridge lets discrete assignments learn end-to-end.
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High-frequency embedding
Dual branches recover detail that low-dimensional transformer inputs can miss.
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Transition sampling
The sampler changes strategy across time as topology turns into texture.
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Recorded run · Sampling trajectory
Inside five
MIND samples.
Five images generated by MIND-XL-G. Every frame decodes the token prediction recorded at that exact step.
Loading complete trajectory0%
v90.31 recorded run · sample 2
001/ 250
Current sampler stateSoft state · argmax visualization
Schedule t0.0010
Visualized tokens16 × 16
Top-k / top-p100 / 0.70
CFG1.0×
CFG off
The high-quality sampler is unchanged. During the first 25 soft steps, argmax tokens are decoded only for visualization; from step 26 onward, the frames show the tokens selected by the original sampling logic.
One-step generation · 600MNoise in.
Noise in.
Image out.
One network evaluation maps a 16 × 16 × 16 continuous latent-noise state to image-token logits, followed by a single tokenizer decode.
InputLatent noise
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Single transitionModel evaluation
→FID0.90
Network evaluations1
CFG1.5×
Checkpoint260K
The input is an exact three-channel projection of the CUDA latent noise used for each selected result—not simulated image-space noise. The brief transition denotes one model evaluation; no intermediate denoising steps are implied.
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Performance · Generated samples
One manifold.
Two sampling regimes.
One-step FD distillation prioritizes speed; multi-step MIND-XL-G achieves stronger distributional fidelity on ImageNet 256 × 256.
Multi-step250 NFE
FID ↓1.84
FDr⁶ ↓4.87
MIND-XL-G · 715M parameters
One-step1 NFE
FID ↓0.90
FDr⁶ ↓6.77
FD-distilled MIND · 600M parameters
FID and FDr⁶: lower is better.
Conclusion