Low-frequency Mamba Fusion Block

• LMFB is a fusion module that allocates low-frequency representations for long-range, global context in architectures, coupling them back to detail-rich streams.
• It employs techniques like discrete wavelet transforms and Laplacian pyramids to extract and process low-frequency components for multi-modal and state-space applications.
• Empirical evidence demonstrates that incorporating LMFB boosts efficiency and accuracy while reducing computational overhead in tasks such as RGB–IR detection and image reconstruction.

Searching arXiv for the cited LMFB-related papers to ground the article. arxiv_search(query="Low-frequency Mamba Fusion Block WaveMamba LMFB (Zhu et al., 24 Jul 2025)", max_results=5) arxiv_search(query="Interactive Spatial-Frequency Fusion Mamba for Multi-Modal Image Fusion (Zhu et al., 4 Feb 2026)", max_results=5) arxiv_search(query="TinyViM Frequency Decoupling for Tiny Hybrid Vision Mamba (Ma et al., 2024)", max_results=5) Low-frequency Mamba Fusion Block (LMFB) denotes a class of Mamba- or state-space-based fusion modules that assign low-frequency representations to the long-range modeling pathway and then couple the resulting global context back to spatial, cross-modal, or high-frequency streams. The term is explicitly used in "WaveMamba: Wavelet-Driven Mamba Fusion for RGB-Infrared Object Detection," where LMFB is the low-frequency submodule inside the WaveMamba Fusion Block (WMFB) (Zhu et al., 24 Jul 2025). Closely related architectures recur across later work under different names: ISFM realizes the same role through the Low-Frequency Fusion Block and frequency-guided gating (Zhu et al., 4 Feb 2026), Laplace-Mamba through its low-frequency Mamba branch (Wang et al., 1 Jul 2025), HiFi-Mamba through the HiFi-Mamba block operating on a wavelet-separated low-frequency stream (Chen et al., 7 Aug 2025), and TinyViM through a Laplace mixer that routes only low-frequency components into SS2D (Ma et al., 2024). This suggests that LMFB is best understood not as a single canonical module, but as a recurrent architectural pattern in frequency-aware Mamba systems.

1. Terminological status and lineage

Only a subset of the literature names an LMFB directly. In WaveMamba, LMFB is a formal component for RGB–infrared low-frequency fusion, paired with a high-frequency enhancement branch inside WMFB (Zhu et al., 24 Jul 2025). In several other papers, the same functional role is present but described through task-specific modules rather than a shared name.

Paper	Explicit naming	LMFB-equivalent mechanism
WaveMamba (Zhu et al., 24 Jul 2025)	Yes	LL fusion via channel swapping, VSS, and DFM
ISFM (Zhu et al., 4 Feb 2026)	No	LFFB plus low-frequency guidance in FGG
Laplace-Mamba (Wang et al., 1 Jul 2025)	No	LFTM→MDFM→LSRB low-frequency branch
HiFi-Mamba (Chen et al., 7 Aug 2025)	No	HiFi-Mamba block on WL low-frequency stream
TinyViM (Ma et al., 2024)	No	Laplace mixer with low-only SS2D branch
DEPF (Li et al., 9 Sep 2025)	No	CSWM-enhanced LL branch before Mamba fusion

The common denominator is the allocation of low-frequency content to the SSM/Mamba pathway because that pathway is used for long-range, global, or low-variance structure. The surrounding fusion logic differs by domain: cross-modal image fusion, dehazing, MRI reconstruction, RGB–IR detection, remote sensing, or BEV perception.

2. Frequency decomposition and the meaning of “low frequency”

In LMFB-type designs, “low frequency” is defined by the transform that precedes Mamba processing. In wavelet-based systems, the low-frequency component is typically the approximation sub-band $LL$. WaveMamba defines

$F_L, F_H = \mathrm{DWT}(I),$

with $F_L=\{F_{LL}\}$ and $F_H=\{F_{LH},F_{HL},F_{HH}\}$, using Haar filters $L=\frac{1}{\sqrt{2}}[1,1]$ and $H=\frac{1}{\sqrt{2}}[1,-1]$ (Zhu et al., 24 Jul 2025). ISFM uses DWT on modality-specific features and explicitly treats the $LL$ branch as low-frequency; its low-frequency fusion starts from

$$X_{lf}=\mathrm{SiLU}(\mathrm{Conv}_{1\times1}(X_{lf}^{ir}+X_{lf}^{vi})).$$

The resulting $X_{ll}^{fuse}$ later guides spatial Mamba fusion (Zhu et al., 4 Feb 2026).

Other formulations replace explicit $LL$ notation with low-pass streams. Laplace-Mamba uses a Laplacian pyramid to produce a downsampled low-frequency component $F_L, F_H = \mathrm{DWT}(I),$0, arguing that the low-frequency branch captures global structures such as background layout, color distribution, and illumination (Wang et al., 1 Jul 2025). HiFi-Mamba uses a wavelet-based W-Laplacian block in feature space, with

$F_L, F_H = \mathrm{DWT}(I),$1

so that a low-pass base and a complementary residual high-pass stream are processed in parallel (Chen et al., 7 Aug 2025). TinyViM achieves a comparable split through average pooling and residual subtraction,

$F_L, F_H = \mathrm{DWT}(I),$2

and feeds only $F_L, F_H = \mathrm{DWT}(I),$3 into SS2D (Ma et al., 2024).

Neighboring frequency-aware Mamba papers broaden this picture. Mamba-FCS uses full log-amplitude FFT features rather than explicit low/high masks, while CVMH-UNet uses DCT-based multi-frequency skip fusion; neither paper defines an LMFB, but both indicate that frequency-structured conditioning can be combined with VSS-based decoding (Wijenayake et al., 11 Aug 2025, Cao et al., 2024). DEPF likewise applies DWT to visible features and uses Mamba scanning on the $F_L, F_H = \mathrm{DWT}(I),$4 branch through CSWM before priority-guided fusion (Li et al., 9 Sep 2025).

3. Canonical computational structure

A typical LMFB can be decomposed into three stages: low-frequency extraction, low-frequency state-space modeling, and reintegration through gating or fusion.

The clearest explicit formulation appears in WaveMamba. At stage $F_L, F_H = \mathrm{DWT}(I),$5, the low-frequency inputs $F_L, F_H = \mathrm{DWT}(I),$6 and $F_L, F_H = \mathrm{DWT}(I),$7 are first mixed by channel swapping,

$F_L, F_H = \mathrm{DWT}(I),$8

then processed by VSS blocks,

$F_L, F_H = \mathrm{DWT}(I),$9

and finally refined by Deep Fusion Mamba,

$F_L=\{F_{LL}\}$0

The DFM uses two information flows for the primary modality, one of which is an SS2D path and the other a lightweight SiLU path, and uses the second flow to regulate both the primary and auxiliary outputs before summation (Zhu et al., 24 Jul 2025).

ISFM exposes a second, more explicitly guided pattern. Its Low-Frequency Fusion Block computes pooled spatial attention

$F_L=\{F_{LL}\}$1

parallel multi-scale depth-wise convolutions

$F_L=\{F_{LL}\}$2

and an attention-weighted residual aggregation

$F_L=\{F_{LL}\}$3

The fused $F_L=\{F_{LL}\}$4 is then injected into the Frequency-Guided Gate, which computes $F_L=\{F_{LL}\}$5 and $F_L=\{F_{LL}\}$6 and modulates Mamba hidden states $F_L=\{F_{LL}\}$7 and $F_L=\{F_{LL}\}$8 through

$F_L=\{F_{LL}\}$9

This coupling makes low-frequency fusion a control signal for spatial Mamba processing rather than merely an auxiliary branch (Zhu et al., 4 Feb 2026).

HiFi-Mamba makes the interaction even more internal to the SSM. It uses the continuous-time form

$F_H=\{F_{LH},F_{HL},F_{HH}\}$0

derives $F_H=\{F_{LH},F_{HL},F_{HH}\}$1, $F_H=\{F_{LH},F_{HL},F_{HH}\}$2, and $F_H=\{F_{LH},F_{HL},F_{HH}\}$3 from the low-frequency sequence, and then additively modulates $F_H=\{F_{LH},F_{HL},F_{HH}\}$4 and $F_H=\{F_{LH},F_{HL},F_{HH}\}$5 with high-frequency guidance $F_H=\{F_{LH},F_{HL},F_{HH}\}$6. The paper explicitly notes that gating $F_H=\{F_{LH},F_{HL},F_{HH}\}$7 degrades stability, so only $F_H=\{F_{LH},F_{HL},F_{HH}\}$8 and $F_H=\{F_{LH},F_{HL},F_{HH}\}$9 are adaptively conditioned (Chen et al., 7 Aug 2025). By contrast, TinyViM adopts a more minimalist LMFB logic: low-frequency tokens alone go to SS2D, high-frequency content is handled by a reparameterized $L=\frac{1}{\sqrt{2}}[1,1]$0 depth-wise convolution, and the two paths are fused by summation and a $L=\frac{1}{\sqrt{2}}[1,1]$1 convolution (Ma et al., 2024).

4. Variants across application domains

In multi-modal image fusion, the LMFB pattern appears as a low-frequency guidance mechanism for reconstructing a fused luminance channel. ISFM takes infrared and visible $L=\frac{1}{\sqrt{2}}[1,1]$2-channel inputs, extracts modality-specific features with VMamba/VSSM blocks, decomposes them by DWT, fuses $L=\frac{1}{\sqrt{2}}[1,1]$3 and high-frequency sub-bands in MFF, and then lets the fused low-frequency component $L=\frac{1}{\sqrt{2}}[1,1]$4 gate Mamba-based spatial fusion in ISF before final reconstruction (Zhu et al., 4 Feb 2026).

In RGB–infrared detection, WaveMamba formalizes LMFB as the low-frequency half of WMFB. The block performs shallow low-frequency interaction through channel swapping and VSS, then deep fusion through SS2D and gated attention, while the high-frequency pathway uses “absolute maximum” selection over $L=\frac{1}{\sqrt{2}}[1,1]$5, $L=\frac{1}{\sqrt{2}}[1,1]$6, and $L=\frac{1}{\sqrt{2}}[1,1]$7. The fused low-frequency outputs are later aggregated and paired with fused high-frequency sub-bands in an IDWT-based detection head (Zhu et al., 24 Jul 2025). DEPF reaches a related endpoint through a different composition: CSWM enhances the visible $L=\frac{1}{\sqrt{2}}[1,1]$8 branch by cross-scale Mamba scanning, optional FDR repairs spectral details, and PGMF performs priority-guided multispectral fusion for UAV detection (Li et al., 9 Sep 2025).

In restoration and reconstruction, LMFB-type modules are used to separate globally coherent structure from detail restoration. Laplace-Mamba assigns the low-frequency branch to a VSSM-based Low-frequency Structure Restoration Block, while a CNN-based HDEB restores edges and textures; the low-frequency output $L=\frac{1}{\sqrt{2}}[1,1]$9 also guides the high-frequency branch through pixel-wise attention (Wang et al., 1 Jul 2025). HiFi-Mamba similarly uses a dual-stream architecture in which the low-frequency stream is the primary input to the HiFi-Mamba block, and high-frequency features are re-injected through adaptive modulation of the SSM’s input and output projections before dual-stream fusion and data-consistency correction (Chen et al., 7 Aug 2025).

In lightweight backbones, TinyViM treats low-frequency Mamba processing as an efficiency mechanism. Its spectral analysis argues that Mamba blocks in hybrid Conv–Mamba architectures mainly model low-frequency information, so the Laplace mixer explicitly routes only the low-frequency component to SS2D while reserving high-frequency enhancement for a mobile-friendly depth-wise convolution branch (Ma et al., 2024).

In broader Mamba fusion systems, the same idea is generalized from explicit frequency bands to global-context propagation. MambaFusion interleaves Mamba SSM blocks with windowed transformers in the LiDAR encoder and uses temporal Mamba over BEV tokens, describing this as propagation of global context in linear time while preserving local geometric fidelity (Narayanan et al., 8 Feb 2026). Mamba-FCS and CVMH-UNet show that frequency-aware fusion can also be implemented with FFT log-amplitude or DCT-based attention around a VSSM backbone, even when no explicit LMFB label is used (Wijenayake et al., 11 Aug 2025, Cao et al., 2024).

5. Empirical evidence

The empirical case for LMFB-type design comes from ablations that isolate low-frequency routing, low-frequency fusion, or low-frequency-guided Mamba modulation.

Paper	Comparison	Reported outcome
WaveMamba (Zhu et al., 24 Jul 2025)	Full LMFB vs. removing SFM or DFM	Full: mAP50 92.1%, mAP 64.4%; no SFM: 90.6%, 62.3%; no DFM: 90.2%, 62.2%
ISFM (Zhu et al., 4 Feb 2026)	MSRS ablation I–V	Best setting $H=\frac{1}{\sqrt{2}}[1,-1]$0: EN 6.70, SF 11.42, AG 3.77, SCD 1.79, VIF 1.01, $H=\frac{1}{\sqrt{2}}[1,-1]$1 0.68
TinyViM (Ma et al., 2024)	Baseline vs. low-only input to Mamba	Top-1 79.1% vs. 79.0%; throughput 1673 vs. 2574 img/s
HiFi-Mamba (Chen et al., 7 Aug 2025)	CC359 AF=8 P2 ablation	WL 27.07 dB / 0.790 SSIM; +LMFB 27.46 / 0.794; +DSFA 27.99 / 0.799; +CRM 28.07 / 0.802

WaveMamba also reports a fusion-strategy ablation on M$H=\frac{1}{\sqrt{2}}[1,-1]$2FD showing that DWT with averaging in both bands yields mAP50 86.6% and mAP 58.2%, whereas replacing low-frequency averaging by LMFB raises these to 90.6% and 62.6%; combining HFE and LMFB reaches 91.0% and 63.3% (Zhu et al., 24 Jul 2025). ISFM reports that “LFFB only” already improves SCD, VIF, and $H=\frac{1}{\sqrt{2}}[1,-1]$3 relative to “no frequency fusion,” and that the addition of FGG, which consumes $H=\frac{1}{\sqrt{2}}[1,-1]$4, yields the best performance among the tested frequency-fusion configurations (Zhu et al., 4 Feb 2026).

In restoration and reconstruction, the same pattern persists. Laplace-Mamba states that replacing LSRB with a residual block degrades PSNR by approximately $H=\frac{1}{\sqrt{2}}[1,-1]$5 dB, while replacing MDFM with naive concatenation also reduces PSNR by approximately $H=\frac{1}{\sqrt{2}}[1,-1]$6 dB, supporting the low-frequency Mamba branch and its learned fusion logic (Wang et al., 1 Jul 2025). HiFi-Mamba reports that its unidirectional, low-frequency-centered Mamba block improves both accuracy and efficiency relative to four-direction Mamba baselines, with HiFi-Mamba(P2) at 67.87G FLOPs versus LMO at 484.98G on fastMRI AF=8 while maintaining stronger reconstruction metrics (Chen et al., 7 Aug 2025).

6. Efficiency, limitations, and open directions

A defining motivation for LMFB is that low-frequency streams are cheaper to process and better matched to linear-time state-space modeling. Several papers realize this directly by reducing the token count before Mamba. Laplace-Mamba processes $H=\frac{1}{\sqrt{2}}[1,-1]$7 at half resolution and reports 0.189 s and 68.90 GFLOPs on $H=\frac{1}{\sqrt{2}}[1,-1]$8 inputs (Wang et al., 1 Jul 2025). TinyViM fixes the Mamba input to a $H=\frac{1}{\sqrt{2}}[1,-1]$9 low-frequency map at every stage and thereby raises throughput to 2574 img/s in the “low only” setting (Ma et al., 2024). HiFi-Mamba replaces four-direction scanning with a single row-major traversal and reports major FLOP reductions while preserving long-range modeling (Chen et al., 7 Aug 2025). ISFM keeps total complexity moderate, with 9.148M parameters, 371 GFLOPs, and 0.28 s runtime on MSRS (Zhu et al., 4 Feb 2026). In the broader spatiotemporal setting, MambaFusion states $LL$0 temporal complexity for $LL$1 frames and $LL$2 tokens, in contrast to $LL$3 attention-based temporal models (Narayanan et al., 8 Feb 2026).

The main limitation is terminological and architectural non-uniformity. LMFB is not a standardized block definition across the literature; the name is explicit in WaveMamba but only approximate in most other papers. Several implementations also omit internal details that would fully determine the block. ISFM does not provide the explicit SSM recurrence or discretization formulas, and it does not define a separate low-frequency-specific loss (Zhu et al., 4 Feb 2026). WaveMamba describes the gated regulation inside DFM qualitatively but does not provide an explicit gate equation (Zhu et al., 24 Jul 2025). MambaFusion references standard selective SSM equations but does not expand the full parameterization used in the kernel (Narayanan et al., 8 Feb 2026).

A second limitation is that low-frequency emphasis alone is insufficient for detail-sensitive tasks. Accordingly, essentially all successful LMFB-type architectures maintain an explicit high-frequency, local, or detail branch: HFE in WaveMamba, HFFB in ISFM, HDEB in Laplace-Mamba, the residual high-frequency stream and DSFA in HiFi-Mamba, and the Rep$LL$4 branch in TinyViM (Zhu et al., 24 Jul 2025, Zhu et al., 4 Feb 2026, Wang et al., 1 Jul 2025, Chen et al., 7 Aug 2025, Ma et al., 2024). This suggests that LMFB is most effective as one half of a complementary low-/high-frequency decomposition rather than as a standalone replacement for full-spectrum fusion.

A plausible implication is that future LMFB research will move toward more explicit band-limited control of the state-space parameters, tighter decoder-level integration, and task-conditioned frequency gating. Such directions are already foreshadowed by the explicit low-/high-band gate derivation proposed around JSFF in Mamba-FCS and by MambaFusion’s suggestion of joint spatiotemporal SSMs deeper in the fusion decoder (Wijenayake et al., 11 Aug 2025, Narayanan et al., 8 Feb 2026).