diff --git a/ggml/src/ggml-cuda.cu b/ggml/src/ggml-cuda.cu
index 895ba4794..2df845234 100644
--- a/ggml/src/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda.cu
@@ -34,7 +34,8 @@
 #include "ggml-cuda/tsembd.cuh"
 #include "ggml-cuda/unary.cuh"
 #include "ggml-cuda/upscale.cuh"
-
+#include "ggml-cuda/ssm_conv.cuh"
+#include "ggml-cuda/ssm_scan.cuh"
 #include <algorithm>
 #include <array>
 #include <atomic>
@@ -2342,6 +2343,11 @@ static bool ggml_cuda_compute_forward(ggml_backend_cuda_context & ctx, struct gg
         case GGML_OP_FLASH_ATTN_EXT:
             ggml_cuda_flash_attn_ext(ctx, dst);
             break;
+        case GGML_OP_SSM_CONV:
+            ggml_cuda_op_ssm_conv(ctx, dst);
+            break;
+        case GGML_OP_SSM_SCAN:
+            ggml_cuda_op_ssm_scan(ctx, dst);
         case GGML_OP_CROSS_ENTROPY_LOSS:
             ggml_cuda_cross_entropy_loss(ctx, dst);
             break;
@@ -2967,6 +2973,8 @@ GGML_CALL static bool ggml_backend_cuda_supports_op(ggml_backend_t backend, cons
         case GGML_OP_ARANGE:
         case GGML_OP_TIMESTEP_EMBEDDING:
         case GGML_OP_LEAKY_RELU:
+        case GGML_OP_SSM_CONV:
+        case GGML_OP_SSM_SCAN:
             return true;
         case GGML_OP_FLASH_ATTN_EXT:
 #if defined(GGML_USE_HIPBLAS) && defined(__HIP_PLATFORM_AMD__)
diff --git a/ggml/src/ggml-cuda/norm.cu b/ggml/src/ggml-cuda/norm.cu
index 133e219f0..f2d643e4e 100644
--- a/ggml/src/ggml-cuda/norm.cu
+++ b/ggml/src/ggml-cuda/norm.cu
@@ -153,9 +153,9 @@ static void group_norm_f32_cuda(const float * x, float * dst, const int num_grou
 }
 
 static void rms_norm_f32_cuda(const float * x, float * dst, const int ncols, const int nrows, const float eps, cudaStream_t stream) {
-    GGML_ASSERT(ncols % WARP_SIZE == 0);
+    GGML_ASSERT(ncols % WARP_SIZE == 0 || ncols < WARP_SIZE);
     if (ncols < 1024) {
-        const dim3 block_dims(WARP_SIZE, 1, 1);
+        const dim3 block_dims(min(ncols, WARP_SIZE), 1, 1);
         rms_norm_f32<WARP_SIZE><<<nrows, block_dims, 0, stream>>>(x, dst, ncols, eps);
     } else {
         const dim3 block_dims(1024, 1, 1);
diff --git a/ggml/src/ggml-cuda/ssm_conv.cu b/ggml/src/ggml-cuda/ssm_conv.cu
new file mode 100644
index 000000000..abb0177f0
--- /dev/null
+++ b/ggml/src/ggml-cuda/ssm_conv.cu
@@ -0,0 +1,100 @@
+#include "ssm_conv.cuh"
+
+template <int block_size>
+static __global__ void ssm_conv_f32(
+    const float * __restrict__ src0, const float * __restrict__ src1,
+    const int src0_nb0, const int src0_nb1, const int src0_nb2,
+    const int src1_nb1,
+    float * __restrict__ dst,
+    const int dst_nb0, const int dst_nb1, const int dst_nb2,
+    const int nc, const int ncs, const int nr, const int n_t, const int n_s) {
+
+    const int tid = blockIdx.y;
+    const int i3 = blockIdx.x;
+    const int i2 = threadIdx.x;
+
+    const int ith = tid;
+    const int nth = WARP_SIZE;
+
+    // rows per thread
+    const int dr = (nr + nth - 1)/nth;
+
+    // row range for this thread
+    const int ir0 = dr*ith;
+    const int ir1 = min(ir0 + dr, nr);
+    const int ir  = ir1 - ir0;
+
+    // {d_conv - 1 + n_t, d_inner, n_seqs}
+    // sliding window
+    const float * s = (const float *) ((const char *) src0 + ir0*src0_nb1 + i2*src0_nb0 + i3*src0_nb2); // {d_conv, d_inner, n_s}
+    const float * c = (const float *) ((const char *) src1 + ir0*src1_nb1); // {d_conv, d_inner}
+    float * x = (float *) ((char *) dst + ir0*dst_nb0 + i2*dst_nb1 + i3*dst_nb2); // {d_inner, n_t, n_s}
+
+    // TODO: transpose the output for smaller strides for big batches?
+    // d_inner
+    for (int i1 = 0; i1 < ir; ++i1) {
+        // rowwise dot product
+        // NOTE: not using ggml_vec_dot_f32, because its sum is in double precision
+        float sumf = 0.0f;
+
+        // d_conv
+        #pragma unroll
+        for (int i0 = 0; i0 < nc; ++i0) {
+            sumf += s[i0 + i1*ncs] * c[i0 + i1*nc];
+        }
+        x[i1] = sumf;
+    }
+}
+
+static void ssm_conv_f32_cuda(
+    const float * src0, const float * src1,
+    const int src0_nb0, const int src0_nb1, const int src0_nb2,
+    const int src1_nb1,
+    float * dst,
+    const int dst_nb0, const int dst_nb1, const int dst_nb2,
+    const int nc, const int ncs, const int nr, const int n_t, const int n_s,
+    cudaStream_t stream) {
+
+    const dim3 block_dims(n_t, 1, 1);
+    //const int nblocks = n_s; // TODO
+    const dim3 grid_dims(n_s, WARP_SIZE, 1);
+
+    ssm_conv_f32<WARP_SIZE><<<grid_dims, block_dims, 0, stream>>>(
+        src0, src1,
+        src0_nb0, src0_nb1, src0_nb2,
+        src1_nb1,
+        dst,
+        dst_nb0, dst_nb1, dst_nb2,
+        nc, ncs, nr, n_t, n_s);
+}
+
+void ggml_cuda_op_ssm_conv(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
+    const struct ggml_tensor * src0 = dst->src[0]; // conv_x
+    const struct ggml_tensor * src1 = dst->src[1]; // conv1d.weight
+
+    const int nc  = src1->ne[0]; // d_conv
+    const int ncs = src0->ne[0]; // d_conv - 1 + n_t
+    const int nr  = src0->ne[1]; // d_inner
+    const int n_t =  dst->ne[1]; // tokens per sequence
+    const int n_s =  dst->ne[2]; // number of sequences in the batch
+
+    GGML_ASSERT( dst->ne[0] == nr);
+    GGML_ASSERT(src0->nb[0] == sizeof(float));
+    GGML_ASSERT(src1->nb[0] == sizeof(float));
+    GGML_ASSERT(src0->nb[1] == src0->ne[0]*sizeof(float));
+
+    const float * src0_d = (const float *)src0->data;
+    const float * src1_d = (const float *)src1->data;
+    float * dst_d = (float *)dst->data;
+    cudaStream_t stream = ctx.stream();
+
+    GGML_ASSERT(src0->type == GGML_TYPE_F32);
+    GGML_ASSERT( dst->type == GGML_TYPE_F32);
+    ssm_conv_f32_cuda(src0_d, src1_d,
+        src0->nb[0], src0->nb[1], src0->nb[2],
+        src1->nb[1],
+        dst_d,
+        dst->nb[0], dst->nb[1], dst->nb[2],
+        nc, ncs, nr, n_t, n_s,
+        stream);
+}
diff --git a/ggml/src/ggml-cuda/ssm_conv.cuh b/ggml/src/ggml-cuda/ssm_conv.cuh
new file mode 100644
index 000000000..8e6c1f00b
--- /dev/null
+++ b/ggml/src/ggml-cuda/ssm_conv.cuh
@@ -0,0 +1,3 @@
+#include "common.cuh"
+
+void ggml_cuda_op_ssm_conv(ggml_backend_cuda_context & ctx, ggml_tensor * dst);
diff --git a/ggml/src/ggml-cuda/ssm_scan.cu b/ggml/src/ggml-cuda/ssm_scan.cu
new file mode 100644
index 000000000..cc8dac9e6
--- /dev/null
+++ b/ggml/src/ggml-cuda/ssm_scan.cu
@@ -0,0 +1,144 @@
+#include "ssm_scan.cuh"
+
+template <int block_size>
+static __global__ void ssm_scan_f32(
+    const float * __restrict__ src0, const float * __restrict__ src1, const float * __restrict__ src2, const float * __restrict__ src3,
+    const float * __restrict__ src4, const float * __restrict__ src5,
+    const int src0_nb1, const int src0_nb2,
+    const int src1_nb0, const int src1_nb1, const int src1_nb2, const int src1_nb3,
+    const int src2_nb0, const int src2_nb1, const int src2_nb2,
+    const int src3_nb1,
+    const int src4_nb1, const int src4_nb2,
+    const int src5_nb1, const int src5_nb2,
+    float * __restrict__ dst,
+    const int nc, const int nr, const int n_t, const int n_s) {
+
+//    const int row = blockIdx.x*blockDim.y + threadIdx.y;
+    const int tid = threadIdx.x;
+    const int i3 = threadIdx.y;
+
+    const int ith = tid;
+    const int nth = WARP_SIZE;
+
+    // rows per thread
+    const int dr = (nr + nth - 1)/nth;
+
+    // row range for this thread
+    const int ir0 = dr*ith;
+    const int ir1 = min(ir0 + dr, nr);
+    const int ir  = ir1 - ir0;
+    for (int i2 = 0; i2 < n_t; ++i2) {
+        const float * s0 = (const float *) ((const char *) src0 + ir0*src0_nb1 + i3*src0_nb2); // {d_state, d_inner, n_s}
+        const float * x  = (const float *) ((const char *) src1 + ir0*src1_nb0 + i2*src1_nb1 + i3*src1_nb2); // {d_inner, n_t, n_s}
+        const float * dt = (const float *) ((const char *) src2 + ir0*src2_nb0 + i2*src2_nb1 + i3*src2_nb2); // {d_inner, n_t, n_s}
+        const float * A  = (const float *) ((const char *) src3 + ir0*src3_nb1); // {d_state, d_inner}
+        const float * B  = (const float *) ((const char *) src4 +  i2*src4_nb1 + i3*src4_nb2); // {d_state, n_t, n_s}
+        const float * C  = (const float *) ((const char *) src5 +  i2*src5_nb1 + i3*src5_nb2); // {d_state, n_t, n_s}
+        float * y = (float *) ((char *) dst + ir0*src1_nb0 + i2*src1_nb1 + i3*src1_nb2); // {d_inner, n_t, n_s}
+        float * s = (float *) ((char *) dst + ir0*src0_nb1 + i3*src0_nb2 + src1_nb3); // {d_state, d_inner, n_s}
+
+        // use the output as the source for the next token-wise iterations
+        if (i2 > 0) { s0 = s; }
+
+        // d_inner
+        for (int i1 = 0; i1 < ir; ++i1) {
+            // ref: https://github.com/state-spaces/mamba/blob/34076d664838588a3c97727b263478ab9f621a07/mamba_ssm/ops/triton/selective_state_update.py#L78
+            float dt_soft_plus = dt[i1] <= 20.0f ? log1pf(expf(dt[i1])) : dt[i1];
+            float x_dt = x[i1] * dt_soft_plus;
+            float sumf = 0.0f;
+            // d_state
+            #pragma unroll
+            for (int i0 = 0; i0 < nc; ++i0) {
+                int i = i0 + i1*nc;
+                // state = prev_state * dA + dB * x
+                float state = (s0[i] * expf(dt_soft_plus * A[i])) + (B[i0] * x_dt);
+                // y = rowwise_dotprod(state, C)
+                sumf += state * C[i0];
+                s[i] = state;
+            }
+            y[i1] = sumf;
+        }
+    }
+}
+
+static void ssm_scan_f32_cuda(
+    const float * src0, const float * src1, const float * src2, const float * src3,
+    const float * src4, const float * src5,
+    const int src0_nb1, const int src0_nb2,
+    const int src1_nb0, const int src1_nb1, const int src1_nb2, const int src1_nb3,
+    const int src2_nb0, const int src2_nb1, const int src2_nb2,
+    const int src3_nb1,
+    const int src4_nb1, const int src4_nb2,
+    const int src5_nb1, const int src5_nb2,
+    float * dst,
+    const int nc, const int nr, const int n_t, const int n_s,
+    cudaStream_t stream) {
+
+    const dim3 block_dims(WARP_SIZE, n_s, 1);
+    const int nblocks = 1; // TODO
+
+    ssm_scan_f32<WARP_SIZE><<<nblocks, block_dims, 0, stream>>>(
+        src0, src1, src2, src3,
+        src4, src5,
+        src0_nb1, src0_nb2,
+        src1_nb0, src1_nb1, src1_nb2, src1_nb3,
+        src2_nb0, src2_nb1, src2_nb2,
+        src3_nb1,
+        src4_nb1, src4_nb2,
+        src5_nb1, src5_nb2,
+        dst,
+        nc, nr, n_t, n_s);
+}
+
+void ggml_cuda_op_ssm_scan(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
+    const struct ggml_tensor * src0 = dst->src[0]; // s
+    const struct ggml_tensor * src1 = dst->src[1]; // x
+    const struct ggml_tensor * src2 = dst->src[2]; // dt
+    const struct ggml_tensor * src3 = dst->src[3]; // A
+    const struct ggml_tensor * src4 = dst->src[4]; // B
+    const struct ggml_tensor * src5 = dst->src[5]; // C
+
+    const int64_t nc  = src0->ne[0]; // d_state
+    const int64_t nr  = src0->ne[1]; // d_inner
+    const int64_t n_t = src1->ne[1]; // number of tokens per sequence
+    const int64_t n_s = src0->ne[2]; // number of sequences in the batch
+
+    GGML_ASSERT(ggml_nelements(src1) + ggml_nelements(src0) == ggml_nelements(dst));
+    GGML_ASSERT(src0->nb[0] == sizeof(float));
+    GGML_ASSERT(src1->nb[0] == sizeof(float));
+    GGML_ASSERT(src2->nb[0] == sizeof(float));
+    GGML_ASSERT(src3->nb[0] == sizeof(float));
+    GGML_ASSERT(src4->nb[0] == sizeof(float));
+    GGML_ASSERT(src5->nb[0] == sizeof(float));
+    // required for the dot product between s and C
+    GGML_ASSERT(src0->nb[1] == src0->ne[0]*sizeof(float));
+    // required for per-sequence offsets for states
+    GGML_ASSERT(src0->nb[2] == src0->ne[0]*src0->ne[1]*sizeof(float));
+    // required to get correct offset for state destination (i.e. src1->nb[3])
+    GGML_ASSERT(src1->nb[3] == src1->ne[0]*src1->ne[1]*src1->ne[2]*sizeof(float));
+
+    const float * src0_d = (const float *)src0->data;
+    const float * src1_d = (const float *)src1->data;
+    const float * src2_d = (const float *)src2->data;
+    const float * src3_d = (const float *)src3->data;
+    const float * src4_d = (const float *)src4->data;
+    const float * src5_d = (const float *)src5->data;
+    float * dst_d = (float *)dst->data;
+    cudaStream_t stream = ctx.stream();
+
+    GGML_ASSERT(src0->type == GGML_TYPE_F32);
+    GGML_ASSERT( dst->type == GGML_TYPE_F32);
+
+    ssm_scan_f32_cuda(
+        src0_d, src1_d, src2_d, src3_d,
+        src4_d, src5_d,
+        src0->nb[1], src0->nb[2],
+        src1->nb[0], src1->nb[1], src1->nb[2], src1->nb[3],
+        src2->nb[0], src2->nb[1], src2->nb[2],
+        src3->nb[1],
+        src4->nb[1], src4->nb[2],
+        src5->nb[1], src5->nb[2],
+        dst_d,
+        nc, nr, n_t, n_s,
+        stream);
+}
diff --git a/ggml/src/ggml-cuda/ssm_scan.cuh b/ggml/src/ggml-cuda/ssm_scan.cuh
new file mode 100644
index 000000000..ee078f5eb
--- /dev/null
+++ b/ggml/src/ggml-cuda/ssm_scan.cuh
@@ -0,0 +1,3 @@
+#include "common.cuh"
+
+void ggml_cuda_op_ssm_scan(ggml_backend_cuda_context & ctx, ggml_tensor * dst);
diff --git a/src/llama.cpp b/src/llama.cpp
index af8afd845..be0da6721 100644
--- a/src/llama.cpp
+++ b/src/llama.cpp
@@ -9590,9 +9590,9 @@ static struct ggml_tensor * llm_build_mamba(
 
         // Some Mamba variants (e.g. FalconMamba) apply RMS norm in B, C & Dt layers
         if (ssm_dt_b_c_rms) {
-            dt = ggml_rms_norm(ctx, dt, norm_rms_eps);
-            B = ggml_rms_norm(ctx, B, norm_rms_eps);
-            C = ggml_rms_norm(ctx, C, norm_rms_eps);
+            dt = ggml_rms_norm(ctx, ggml_cont(ctx, dt), norm_rms_eps);
+            B = ggml_rms_norm(ctx, ggml_cont(ctx, B), norm_rms_eps);
+            C = ggml_rms_norm(ctx, ggml_cont(ctx, C), norm_rms_eps);
         }
 
         // {dt_rank, d_inner} @ {dt_rank, n_seq_tokens, n_seqs} => {d_inner, n_seq_tokens, n_seqs}