Cross-attention is the primary interface through which text conditions latent diffusion models, yet its step-wise multi-resolution dynamics remain under-characterized, limiting principled training-free control. We cast diffusion cross-attention as a spatiotemporal signal on the latent grid by summarizing token-softmax weights into token-agnostic concentration maps and tracking their radially binned Fourier power over denoising. Across prompts and seeds, encoder cross-attention exhibits a consistent coarse-to-fine spectral progression, yielding a stable time-frequency fingerprint of token competition. Building on this structure, we introduce Attention Frequency Modulation (AFM), a plug-and-play inference-time intervention that edits token-wise pre-softmax cross-attention logits in the Fourier domain: low- and high-frequency bands are reweighted with a progress-aligned schedule and can be adaptively gated by token-allocation entropy, before the token softmax. AFM provides a continuous handle to bias the spatial scale of token-competition patterns without retraining, prompt editing, or parameter updates. Experiments on Stable Diffusion show that AFM reliably redistributes attention spectra and produces substantial visual edits while largely preserving semantic alignment. Finally, we find that entropy mainly acts as an adaptive gain on the same frequency-based edit rather than an independent control axis.
Figures & tables
Figure 3: Quantitative summary of coarse-to-fine and AFM effects (encoder, top- K ). (a) uses denoising progress u(s) (early → late); tick labels show decreasing DDIM timesteps τs . (b) shows radial energy profiles over normalized radius r .
Stage
Neg. pairs (%)
Mean Δρlate (min–max)
Encoder
98–99
[ −0.063,−0.040 ]
Middle
72–78
[ −0.0346,−0.0317 ]
Decoder
56–64
[ −0.0161,−0.0092 ]
Table 1: Robustness of late-stage HF-ratio shift Δρlate across rc∈{0.20,0.25,0.30} and Nsub∈{50,100} (top- K=8 ). Δρlate is averaged over the last 20% denoising steps ( u≥0.8 ). AFM is applied only to the encoder cross-attention; middle/decoder reflect downstream changes. We report the fraction of pairs with Δρlate<0 and the min–max range of the mean Δρlate across sweeps.
SD v1.5
SD v1.4
Comparison
COCO
LAION
COCO
LAION
Baseline vs. AFM-curve
0.237 ± 0.138
0.249 ± 0.142
0.232 ± 0.132
0.258 ± 0.144
Baseline vs. AFM-curve + entropy
0.409 ± 0.131
0.419 ± 0.149
0.405 ± 0.134
0.417 ± 0.143
Baseline vs. Baseline (entropy, λ=0 )
0.000 ± 0.000
0.000 ± 0.000
0.000 ± 0.000
0.000 ± 0.000
Baseline vs. FreeU
0.300 ± 0.131
0.302 ± 0.158
0.296 ± 0.117
0.294 ± 0.112
Baseline vs. SAG
0.111 ± 0.084
0.125 ± 0.108
0.106 ± 0.055
0.121 ± 0.071
Table 2: Paired LPIPS ↑ (mean ± std) under matched prompt/seed sampling. Higher indicates larger perceptual deviation from Baseline. Results are reported for SD v1.5 (main) and SD v1.4 (checkpoint robustness).
Setting
LPIPS low
LPIPS high
High/Low
P(high>low)
AFM-curve
0.171 ± 0.115
0.188 ± 0.112
1.21 ± 0.28
78.0%
AFM-curve + entropy
0.312 ± 0.116
0.329 ± 0.110
1.08 ± 0.15
72.5%
Entropy only ( λ=0 )
0.000 ± 0.000
0.000 ± 0.000
–
–
Table 3: Band-wise LPIPS decomposition (COCO; N=200 ). We decompose each output image into Ilow=Gσ(I) (Gaussian blur; σ=4 at 512×512 ) and Ihigh=clip[0,1](I−Ilow+0.5) , and compute LPIPS on each band after resizing to 256×256 . LPIPS low proxies structure/layout change and LPIPS high proxies detail/texture change. High/Low is the per-pair ratio LPIPS high /LPIPS low averaged over pairs (undefined for the exact no-op). P(high>low) is the fraction of pairs where LPIPS high exceeds LPIPS low .
SD v1.5
SD v1.4
Setting
COCO
LAION
COCO
LAION
Baseline
0.318 ± 0.031
0.306 ± 0.038
0.320 ± 0.027
0.306 ± 0.039
AFM-curve
0.319 ± 0.030
0.306 ± 0.039
0.318 ± 0.029
0.304 ± 0.040
AFM-curve + entropy
0.316 ± 0.030
0.303 ± 0.040
0.317 ± 0.030
0.303 ± 0.038
FreeU
0.307 ± 0.031
0.310 ± 0.037
0.307 ± 0.029
0.310 ± 0.034
SAG
0.305 ± 0.032
0.307 ± 0.036
0.304 ± 0.029
0.308 ± 0.033
Table 4: CLIP cosine similarity ↑ (ViT-B/32; mean ± std) under matched prompt/seed sampling. Higher indicates better text–image alignment. Results are reported for SD v1.5 (main) and SD v1.4 (checkpoint robustness).